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Advisory Board and Editors

Front Title

Santra, S B

Deb, D

Indian I Phys. 82 (3), 295-302 (2008) 
Sandpile under rotational constraint 
S B Santra* and D Deb 
Department of Physics, Indian Institute of Technology Guwahati, 
Guwahati-781 039, Assam, India 
E-mail santrafa ntg ernet in 
Abstract Sandpile model is studied here imposing rotational constraint on the flow of sand grains The 
rotational constraint is constituted by certain deterministic rules The rotational dynamics evolves the system into 
a non-equilibrium steady state characterized by power law correlations and exhibits self organized criticality 
The exponents characterizing the power law distributions of avalanche properties are found different from 
other models Consequently the present model belongs to a new universality class 
Keywords Sandpile, self-organized criticality, rotational constraint 
PACS Nos. 45 70 Cc, 05 65 +b 
1. Introduction 
The phenomenon that a class of externally driven systems evolves naturally into a state 
of no single characteristic size or time is known as self-organized criticality (SOC) [1]. 
The non-equilibrium steady state in SOC is characterized by long range spatio-temporal 
correlations and power law scaling behavior. SOC was established for the first time through 
sandpile model by Bak, Tang and Wiesenfeld (BTW) [2]. Sandpile then became a 
prototypical model for studying SOC. The model was studied widely and many results are 
available in the literature [3]. A variant of BTW model is Manna's stochastic model (MSM) 
[4]. In MSM, sand grains flow in randomly selected directions rather than in all possible 
direction on a lattice as in BTW. Extensive attention has also been paid to MSM. It was 
a controversial issue over a period of time whether MSM belong to the same universality 
class of BTW or not [5]. In MSM, the distribution functions of avalanche properties obey 
finite size scaling (FSS) whereas in BTW, some of them obey multi-scaling rather than 
FSS. Recently, it has been concluded that MSM belongs to a different universality class 
than that of BTW from moment analysis of the avalanche distribution functions [6-8]. 
Corresponding Author 
© 2008 IACS 
296 S B Santra and D Deb 
In this paper, a new two state sandpile model is constructed imposing rotational 
constraint on the flow of sand grains. In this rotational sandpile model (RSM), the toppling 
rules are deterministic except at the very first toppling. A site topple if it exceeds the 
predefined critical height and two sand grains flow in the forward direction or in a specific 
rotational direction, say clockwise. A physical realization of RSM could be a sandpile on 
a rotating disk where the disk is rotating about an axis perpendicular to the plane of the 
disk and passing through the center of the disk. It is found that the rotational dynamics 
adopted here evolves the system into a non-equilibrium steady state at which the average 
height of the sandpile remains constant. The spatio-temporal correlations in the non-
equilibrium steady state of RSM are characterized by power law distributions. 
2. Rotational sandpile model 
RSM is defined here on a square lattice in two dimensions (2D). A positive integer ht is 
assigned to each lattice site, called the height of the site. Initially, all the hp are set to 
zero. Sand grains are added to randomly chosen lattice sites and the variable ft, is 
incremented to ft, + 1 if a sand grain is added to the / th site. A site is called active 
when the height of a site becomes greater than or equal to a predefined threshold value 
hc = 2, as in MSM. Toppling of the first active site initiates an avalanche. This site can 
be called the origin of the avalanche. On the very first toppling of the active site, two sand 
grains are given away to two randomly selected nearest neighbors out of four nearest 
neighbors on a square lattice. As soon as a site receives a sand grain, the direction dl 
from which the grain was received is assigned to it along with the increment of its height 
ft,. The value of dt can change from 1 to 4 as there are four possible directions on the 
square lattice. As the avalanche propagates, the direction d{ and height ft, are updated on 
receiving a sand grain and only the information from which direction the last sand grain 
was received is kept. The next active site with ft,. > 2 in the avalanche will topple and two 
sand grains will flow in the direction from which the last grain was received and to a 
clockwise rotational direction. The toppling rules can be stated as 
ft, - > f t , - 2 
fty-*fty+1, y = d, & d,+1 (1) 
where d, is the direction from which the last sand grain was received by the /th site. If J 
becomes greater than 4 it is taken to be 1. Toppling of active sites are then made 
deterministically in this model except at the origin. The propagation of the avalanche 
stops if all sites in the lattice become under critical. The duration or lifetime of an avalanche 
is taken as the number of parallel updates to make all the sites under critical. The 
avalanche dynamics is studied with the open boundary condition. During an avalanche no 
sand grain is added. The steady state of this dynamical system corresponds to the 
constant average height of the sandpile. 
Sandpile under rotational constraint 297 
A typical avalanche obtained in the steady state of RSM on a square lattice of size L 
= 128 is shown in Figure 1. The grey level of a site depends on the number of times it 
has toppled It is found here that the number of toppling of a single active site varies from 
1 to the order of lattice size L In Figure 1, bright grey level corresponds to the maximum 
number of toppling and dark grey level corresponds to the minimum number of toppling 
Figure 1. A typical RSM avalanche generated on a square lattice of size 128 x 128 is shown The grey 
level of a site depends on the number of times it has toppled Low grey level corresponds to the maximum 
number of toppling and high grey level corresponds to the minimum number of toppling, le one White 
space inside the avalanche corresponds to the sites that did not topple at all during the avalanche The 
area of the avalanche is 12256, total number of toppling is 211992 and the maximum number of toppling 
of a site is 68 
White space inside the avalanche corresponds to the sites that did not topple at all 
during the avalanche. It can be seen that there are more than one bright spots along with 
mixing of grey levels The occurrence of several bright spots and mixing of grey levels 
indicates that there are several regions of higher number of toppling surrounded by regions 
of lower number of toppling. The regions of lower number of toppling may exist inside the 
region of higher number of toppling. This is unusual in BTW model [9] However this 
happens in MSM since sand flows stochastically [4] This is demonstrated for both BTW 
and MSM by Ben-Hur and Biham [5]. It can also be noticed that there are several white 
space or holes (no toppling region) inside the avalanche. In BTW, the avalanches are 
compact and do not include any hole inside avalanche [9] However, there exist some 
holes inside the avalanche in Manna's directed model [10] Thus, the avalanche cluster is 
similar to that of MSM even though the toppling rules are deterministic here in RSM The 
final state in an avalanche will depend on the sequence of toppling due to the deterministic 
rules considered here. Consequently, the model in nonabelian like MSM 
RSM is thus a new two state deterministic nonabelian sandpile model It is then 
interesting to characterize the avalanche properties of RSM at its non-equilibrium steady 
298 S B Santra and D Deb 
state. Below, the steady state of RSM is characterized by calculating the probability 
distributions of avalanche properties. 
3. Results and discussion 
The non-equilibrium steady state is defined by the constant average height of the sandpile 
at which the rate of influx of sand grain to the system is equal to the rate of out flux at 
the open boundary. In order to identify the steady state the average height 
(h) = ith> (2) 
has been measured generating 106 avalanches. The average height <h> is plotted against 
the number of avalanches in Figure 2 for L = 2048. It can be seen that a constant 
average height is obtained. The value of <h> remains constant over a large number of 
avalanches. For smaller lattice sizes the steady states are reached by smaller number of 
avalanches. A slight variation of the average height with the system size is observed. The 
values of <h> against the system size are shown in the inset. In order to characterize 
the physical properties of the avalanches occurred at the steady, simulations have been 
performed on the square lattice of sizes L = 128 to L = 2048 in multiple of 2. First 10b 
avalanches were skipped to achieve the steady state. Extensive data collection have 
made for each lattice size for averaging, ranging from 32 x 106 avalanches for L = 128 
down to 2 x 106 avalanches for L = 2048 in ten configurations. In each configuration the 
initial 105 avalanches are neglected again at the steady state before collecting data. 
07 
rip J 
5x10s 
number of avalanche 
10x10s 
Figure 2. Plot of average height <h> against the number of avalanches. The value of <h> remains 
constant over a large number of avalanches and changes slightly with the system size L Dependence of 
<h> on the system size L is shown in the inset. 
The characterization of the physical properties of the avalanches occurred at the steady 
state are made by measuring : the total number of toppling s, the area a of the avalanche, 
the lifetime t of an avalanche and the spatial extension of the avalanche /. The probability 
Sandpile under rotational constraint 299 
distributions of all these properties (s,a,t,l) are determined. The probability distribution 
functions of the avalanche related quantities at the steady state are expected to obey 
power law behavior 
P(x) (3) 
where rx is the corresponding critical exponent and x stands for s,a,t and / Data are 
collected in bins of 10s, 100s, 1000s and so on and finally it is normalize by hin widths 
In Figure 3, the probability distribution P(x) is plotted against x where x corresponds to 
toppling numbers s (diamonds), area a (circles), life time t (triangles) and spatial extension 
/ (squares). It can be seen that the distributions F\x) follow reasonable power law behavior 
for each property x The values of the associated critical exponents rx are obtained as 
r„ - 1 224 ± 0.003, ra = 1.334 ± 0.004, T, = 1 389 ± 0 005 and r, = 1 667 ± 0 005 The 
error bars quoted here are the least square fitting errors taking into account of statistical 
error of each data point In the inset of Figure 3, the distribution of scaling numbers P(s) 
are plotted against s for different lattice sizes It can be seen that the same power law 
behavior is obtained for all the system sizes L The slope obtained for different L is within 
the error bar already mentioned with the respective exponents The values of the exponents 
for BTW are rs - 1 293, ra - 1 330, rt - 1,480 and T, ~ 1 665 and for MSM they are 
rs - 1.275, ra - 1 373, rt * 1 493 and r, - 1 743 The values of the exponents for 
BTW and MSM taken from Ref [5,11,12] Interestingly, the toppling number exponent rs 
and the lifetime exponent rt are only slightly different from that of BTW whereas ra and 
tj are almost the same. The disagreement of the lifetime and toppling distribution exponents 
with that of the BTW exponents can be accounted by the fact that in RSM the avalanche 
waves generally have a spiraling nature around some regions within the avalanche cluster 
and as a consequence it will take longer time and large number of topplings for an 
o 
o 
9 
-6 
-12 
0 0 4 0 80 
iog10x 
Figure 3. Plot of probability distributions of number of toppling in an avalanche P(s) (o ) , avalanche area 
P(a) (O), lifetime P(f) ( A ) and extension of avalanche P(/) ( D ) against the corresponding variables s, a, 
t and / Reasonable power law distributions are obtained for all the properties In the inset, P(s) is plotted 
against s for different system size L 
300 S B Santra and D Deb 
avalanche to die away than that in BTW. On the other hand, in comparison to MSM 
most of the exponents are found different. Note that rs = 2 - 1/ra , conjectured by Majumder 
and Dhar [13], is satisfied by in case of MSM The conjecture is found not valid for BTW 
It can be seen that the conjecture is also not valid in case of RSM. The expected value 
of *, in RSM form the conjecture is « 1.25 outside the error bar of the obtained value 
1.224 ± 0.003. Thus, from the point of power law correlations, the avalanche properties 
are close to that of BTW and different from MSM. 
Since the avalanche properties are related to each other, conditional expectation values 
can be defined. The conditional expectation value of an avalanche property x when another 
property is exactly equal to y is defined as 
(x(y)) = £xP(x,y)
 (4) 
where P(x,y) is the probability to find a property x when the other property is exactly 
equal to y. It is expected that the expectation values will scale with its argument as 
(x(y)) ~ yy« • (5) 
Four expectation values (s(a)) ~ au\ (a{t)) ~ tY«
 t (a(/)) ~ lY« and t(l) ~ lYtl are 
calculated on a square lattice of size L = 2048 and their scaling behavior are determined 
In Figure 4, the expectation values are plotted against their arguments in order to evaluate 
the exponents Yxy. From the best fitted straight lines the estimated values of the exponents 
are Ysa = 1.453 ± 0 003, Yat = 1 167 ± 0 005, Yai = 2 002 ± 0 002 and Yti = 1 715 ± 
0 005 The values of the exponents for BTW are ysa ~ 1.06, yat « 1 53, ya/ « 2 and 
Yti = 1.32 and for MSM they are : ysa = 1.23, yaf «1.35, ya/ « 2 and yn = 1 49 The 
8 
lo8ioy 
Figure 4. Plot of inter dependence of avalanche properties toppling (s) versus area (a) (+), area (a) 
versus extension (/) (O), area (a) versus time (/) (a) and time (0 versus length (/) (A) The solid line 
shows the best fitted straight line part 
Sandpile under rotational constraint 301 
values of the exponents for BTW and MSM are taken form the Ref. [5,11,12]. There are 
few things to notice. First, Ysa is found greater than one and a relevant exponent. This is 
expected because in this model, a site topples many times in an avalanche due to 
rotational constraint. Second, the exponent Yai is found ~ 2 since the avalanches are 
almost compact with a very few holes here and there. This is also the case for other 
models. Third, the value of the dynamical exponent Yti is the highest in RSM and it is 
lowest in BTW. Since Yxy = ^Yyx, the inverse of the dynamical exponent is ylt which 
describes the diffusion of sand grains with respect to time. In that case, diffusion will be 
slowest in RSM and it will be fastest in BTW. This is expected. Because, the rotational 
constraint takes the sand grains into the interior of the system. Fourth, according to the 
scaling form given in eq. 5, the exponents should satisfy the scaling relation Yxz = YxyYyz. 
It can be seen that the scaling relation Yai = YatYti is satisfied within error bars. Fifth, the 
values of YSa> Yat and yf/ are found different from that of BTW as well as MSM except 
Yai- Finally, a set of scaling relations between the distribution exponents rx and the 
exponents Yxy describing the conditional expectation values of the avalanche properties 
can be obtained from the following identiy 
j(x(y))P(y)dy = j(x(z))P(z)dz (6) 
which would be satisfied by any set of three stochastic variables x, y and z. Using this 
identify and the relation Yxz = YXyYyz, the following scaling relation can be obtained 
Yxy=(Yy-l)/(Yx-l)- (7) 
The above scaling relations for x.ye {s,a,l,t) are satisfied within error bars for the 
numerical values obtained here. Thus, the exponents obtained here in RSM are consistent 
with the scaling relations but different from that of the BTW as well as MSM. It indicates 
that RSM belongs to a new universality class. In a recent study, Biham et al [T4^ showed 
a crossover behavior of critical exponents from Zhang model [15] to that of BTW model 
[2] depending upon a non-universal parameter p, the probability of sand flow in a given 
direction. 
Following Karmakar et al [10], moment analysis of avalanche properties, 
(x9) = jxqP(x,L)dx * L^ (Q), have been performed. It is found that RSM follows finite size 
scaling like MSM rather than multi scaling like BTW. This observation is also supported 
by the negative time autocorrelation of toppling waves constituting avalanche. 
4. Conclusion 
A new two state deterministic sandpile model. RSM, is defined imposing rotational constraint 
on the original BTW model. The non-equilibrium steady state of RSM is charaterized by 
power law distribution of avalanche properties and exhibits SOC. The exponents describing 
302 S B Santra and D Deb 
the power laws are found close to that of BTW. The values of the exponents satisfy the 
scaling relations among them within error bars. The rotational sandpile model therefore 
does not belong either in BTW or in MSM. RSM then belongs to a new universality 
class. 
Acknowledgment 
This work is financially supported by BRNS, DAE, India, grant no. 2005/37/5/BRNS. 
References 
[1] H J Jensen Self-Organized Criticaiity (Cambridge) (1998) 
[2] P Bak, C Tang and K Wiesenfeld Phys. Rev. Lett 59 381 (1987) 
[3] D Dhar Physics A263 4 (1999) and references therein. 
[4] S S Manna J Phys A • Math Gen 24 L363 (1991) ; Physics A179 249 (1991) 
[5] A Ben-Hur and O Biham Phys. Rev. E53 R1317 (1996) 
[6] C Tebaldi, M De Menech and A L Stella Phys. Rev Lett 83 3952 (1999) 
[7] S Lubeck Phys. Rev. E61 204 (2000) 
[8] R Karmakar and S S Manna Phys. Rev E71 R015101 (2005) 
[9] P Grassberger and S S Manna J. Phys (Pans) 51 1077 (1990); S Banerjee, S B Santra and i 
Bose Z Phys. B96 571 (1995) 
[10] R Karmakar, S S Manna and A Stella Phys. Rev. Lett 94 088002 (2005) 
[11] S Lubeck and K D Usadel Phys. Rev. E55 4095 (1997) 
[12] A Chessa, H E Stanley, A Vespignani and S Zappen Phys. Rev. E59 R12 (1999) 
[13] S N Majumder and D Dhar Physica A185 129 (1992) 
[14] O Biham, E Milshtein and O Malcai Phys. Rev E63 061309 (2001) 
[15] Y C Zhang Phys. Rev. Lett 63 470 (1989)

English

Sandpile Under Rotational Constraint

Singh, Krishna Kumar

Singh, Shubha

Patel, R P

Singh, Jaipal

Singh, A K

Singh, Ashok K

Singh, R P

Lalmani

Indian J Phys. 82(4) 379-386(2008) 
# 
Estimation of magnetospheric electron densities from low 
latitude whistlers 
Krishna Kumar Singh1, Shubha Singh1*, R P Patel1, Jaipal Singh2, A K Singh1, 
Ashok K Singh3, R P Singh1 4 and Lalmani5 
Atmospheric Research Laboratory, Department of Physics, Banaras Hindu University, Varanasi 221 005, 
Uttar Pradesh, India 
-Department of Physics, G G M Science College, Canal Road, Jammu 180 001, Jammu & Kashmir, India 
-^ Department of Physics, Lucknow University Lucknow 226 007, Uttar Pradesh, India 
4Veer Kunwar Singh University, Ara-802 301, Bihar, India 
^Department of Physics, National Institute of Technology Hazratbal Srinagar Kashmir-190 006 
Jammu & Kashmir, India 
E-mail singhshubhabhu®gmail com 
Received 27 February 2007 accepted 20 December 2007 
Abstract : Dispersion analysis of whistler waves recorded at the low latitude stations have been used to 
estimate electron density in the equatorial region and electron contents in the flux tube aligned along the dipolar 
geomagnetic fields lines This is possible only when waves have propagated along the field lines In this paper, 
we report some examples of whistler waves recorded at the ground station Jammu (geom lat 22° 26' N, L = 
1 17) India, whose analysis yield path of propagation in the range 1 62 < L < 4 39 The matched filtering and 
parameter estimation technique has been used to analyze these whistlers and the error in estimating the path 
of propagation is less than 3% However, the computed electron densities and electron tube contents based on 
the analysis of these whistlers are found to be one order of magnitude smaller than the values reported by the 
other workers This shows that the matching of simulated and observed dynamic spectra need not necessarily 
yield correct path of propagation and hence correct value of electron density As a result either the propagation 
mechanism at low latitude or the analysis method of whistlers recorded at low latitudes has to be reconsidered 
Keywords : Matched filtering, zero frequency dispersion, wave-normal, whistler mode, electromagnetic wave 
propagation, lonosphere-magnetosphere interaction 
PACS Nos. : 94.30 -d, 94 30 Tz, 94 30 Hn, 94 20 Wg, 94 20 Wj 
1. Introduction 
The analysis of whistler dispersion yields information about the medium parameters 
such as electron density, total electron content of flux tube [1-9], electron temperature 
[10-13], magnetic field and large-scale electric field [14-16,2]. In the estimation of 
these parameters it is assumed that the whistler mode signal has propagated in the 
ducted mode along the dipolar geomagnetic field lines and the plasma distribution 
'Corresponding Author ® 2 0 0 8 I A C S 
380 Krishna Kumar Singh et a; 
follows a given model. The most widely used model is the diffusive equilibrium mode' 
[17]. Using the usual technique of dispersion analysis some efforts were made to 
estimate the equatorial electron density and total electron contents in the plasmasphere 
by analyzing whistlers recorded at the low latitude Indian stations [18-20,9,16]. Singh 
et al [21,22] analyzed some selected whistlers recorded at Varanasi using the matched 
filtering and parameter estimation technique and showed the validity of the technique 
in analyzing whistler signals recorded at low latitudes. In this technique also it is 
assumed that the wave has propagated along the dipolar geomagnetic field line The 
accuracy depends on the accurate reproduction of the observed dynamic spectra 
using initial parameters such as zero frequency dispersion, initial time delay and nose 
frequency. However, using the same technique the results of analysis in some cases 
show anomalous behavior as far as the relation between L-value and dispersion is 
concerned [23]. In the normal case dispersion is proportional to the length of path 
covered by the wave i.e. L-value. As L-value increases dispersion increases. 
At this stage we are not able to improve either the model of electron 
distribution, when compared with that used by [21,22,24] or the measurement accuracy 
of whistler parameters for low latitudes based on the analysis to a limited number of 
whistlers recorded at other low latitude Indian ground stations. However, it seems 
useful to extend the analysis to a larger number of whistlers recorded at Jammu in 
order to get some feelings about the probing potentiality of whistlers recorded at the 
low latitudes and their applicability. In this paper we present the variation of equatorial 
electron density and total electron contents with L-value derived from the analysis o! 
22 whistlers recorded at Jammu during the night hours. An example of whistler 
spectrograms of a typical event used in the present study is shown in Figure 1, which 
occurred in the pre-midnight sector on June 5, 1997 during deep quieting period 
(average KP ~ 1). Whistler data used in the dispersion analysis are presented in 
Section 2. Results of the analysis are discussed in Section 3. The main conclusion 
of the paper is given in Section 4. 
2. Whistler data and analysis 
Jammu station is well equipped for the measurements of VLF waves from natural 
sources. Broad band VLF signals are received by a T-type antenna, amplifiers and 
tape recorder with bandwidth from 50 Hz to 15 kHz. The antenna is erected at a 
suitable distance from the main building to reduce the power line hum and any other 
type of man made noises. Between the antenna and pre/main amplifier, an active filter 
unit is introduced to reduce the local noise to a minimum in the frequency range from 
100 Hz to 500 Hz. The gain of the pre/main amplifier is varied form 0 to 40 dB to 
avoid over loading of the amplifier at the time of intense whistler activity. The 
observations were taken continuously during day and nighttimes under AICPITS 
program and whistlers in large numbers were observed during night hours. The 
estimation of magnetosphenc electron densities from low latitude whistlers 
JAMMU05 06 97 22 12 LT 
381 
- 2 
1 0 12 
t (sec) 
1 4 1 6 1 8 2 0 2 2 
Figure 1 Spectrogram of one of the whistler events (as an example) received at Jammu on June 5 1997 at 
? 12 1ST which are analysed in this paper alongwith other whistler events Whistlers numbered 1-7 in Table 1 
ve marked by A, B C, D, E, F and G 
whistler data were stored in analog form on magnetic tapes, which were analyzed 
jsing a digital sonograph having variable frequency range from 100 Hz to 40 kHz 
During the span of seven years of recording periods, we could observe several 
hundreds of whistlers during night hours The dates and times of 22 short whistlers 
recorded at Jammu, which we used in the present study are shown in Table 1 Short 
whistlers are analyzed using matched filtering and parameter estimation technique 
f21 22,24,25] and various magnetosphenc parameters are derived The results are 
also shown in Table 1 
3 Results and discussions 
Dispersion values of analyzed whistlers reported in Table 1 lies between 11 9 and 88 9 
sw whereas the corresponding L-value lies between 1 6 and 4 4 This shows that the 
reported whistlers belong to mid latitude phenomena From Table 1, we find discrepancy 
between the dispersion of whistler waves and corresponding derived L-value [23] The 
L-value of the Jammu station is 1.17. Therefore, the derived L-value greater than 1 2 
•mplies that the waves may have propagated along higher L-value, and after exiting 
form the duct, might have penetrated the ionosphere and were trapped in the earth-
,0nosphere wave guide. The wave-normal at the entrance into the wave guide was 
<Such that they propagated towards the equator and were received at low-latitude 
tat|on Jammu [26,8]. Some of the whistlers for which the L-value and dispersion do 
IQt match, may have leaked from the duct in the magnetosphere and followed another 
l th
 »n the magnetosphere and propagated to the recording station It clearly shows 
384 Krishna Kumar Singh & % 
The variation of total electron content in a flux tube (NT) with L-value denvea 
from whistler data of Jammu, Varanasi, Tihany and Siple is presented in Figure 3 1 
is clearly seen that the total electron content derived from the data of Varanasi ana 
Jammu is lower than those of Tihany and Siple The four data point of Jammu shov 
higher value and in the range of Siple data when extended to L - 44 . Analyzing 
whistler data recorded at low latitude Indian stations, Indian Scientists [9,19,20 29 
have reported that the total electron content in a flux tube ~101 3 electrons cm 
tube 1 during night times The analyses of whistlers always yield the electron density 
B 5 
CM 
E o 
o 4 | -
x 
LU 
Z 
o 
o 
o 
DC 
o 
LD 
- J 
LL1 
-J 
< 
3 
2 h 
[-
k 
I 
• 
r * + 
0 
I I 
# 
* 
t 
L. 
a 
Oft 
+ Tihany (Oct - Feb 70-74) 
• Tihany (March - Aug 72-75) 
O Siple (1973) 
o Jammu (Dec 1996 Dec 2003) 
• Varanasi (March 1991 - Feb 1997) 
D 
O 
1 • 
? • * « t f 4 > * o°
 l 
o • 0 
1 
1 
I 
1 
1 
o , 
• 
I 
1 
1 2 1 5 2 25 3 35 4 45 
L-VALUE 
Figure 3. Variation of total electron content (electrons cm 2 tube 1) in a flux tube with L-value 
of the ducting structures At L > 2, density enhancements of the order of 10% are 
sufficient to produce ducted propagation, whereas at low latitudes (L < 2) enhancement 
factors of - 1 0 0 % are required for the ducted propagation of whistlers [30,31] As the 
propagation at low latitudes is in the non-ducted mode, the estimation of electron 
density and total electron contents in a flux tube becomes erratic Because if the 
signals have propagated strictly along the dipolar field lines in prolongitudmal mode 
then the method of estimation of electron density could be used and estimated value 
truly represents the electron density and total electron contents along the path of 
propagation. The derived lower value suggests a relook in the propagation mechanism 
of whistler mode signals, which has been suggested by others [27,23]. Ferencz et al 
[27] have analyzed a large number of whistlers recorded at mid latitude station 
Bornholm Island and showed that there was mismatch in the L-value of recording and 
Estimation ofmagnetosphenc electron densities from low latitude whistlers 385 
derived L-value from the analysis of whistlers using Match Filtering and Parameter 
Estimation Technique (MFPE) which is also used in the present analysis However, 
they have not estimated electron density Singh et al, [23] have analyzed whistlers 
recorded at Jammu using Match Filtering and Parameter Estimation Technique (MFPE) 
and have discussed only discrepancy in L-value and dispersion values 
4 Conclusion 
in the present paper we have derived the electron clensity distribution and total 
electron content in the flux tube using Match Filtering and Parameter Estimation 
Technique (MFPE) and found that these parameters are about one order of magnitude 
smaller than those derived from the whistlers recorded at mid and high latitudes This 
shows that the analysis method is based on field aligned propagation is not capable 
to depict correct picture of VLF propagation at low latitudes Therefore, a proper 
analysis method should be developed Further, the propagation mechanism of whistler 
mcde signals at low latitudes should be studied in detail including the effect of 
mhomogeneity in the medium parameters and the curvature in the geomagnetic field 
lines 
Acknowledgment 
Krishna Kumar Singh is thankful to CSIR, New Delhi for providing the financial 
assistance R P Patel is thankful to Department of Science and Technology, Government 
of India, New Delhi for awarding research project under SERC-Fast Track Scheme for 
young Scientists (SR/FTP/PS-12/2006) The work is partly supported by DST, New 
Delhi under SERC project One of the authors Mr Jaipal Singh is thankful to their 
Principal Dr R L Sharma of G G M Science College, Jammu for his kind help and 
support 
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[9] R P Singh, Lalmani and U P Singh Ann Geophys 11 1011 (1993) 
[10] F L Scarf Phys Fluids 5 6 (1962) 
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[12] S S Sazhm, A J Smith and E M Sazhm Ann Geophys 8 273 (1990) 
[13] S S Sazhm, P Bognar, A J Smith and Gy Tarcsai Ann Geophys 11 619 (1993) 
386 Krishna Kumar Singh et ai 
[14] LP Block and D L Carpenter J Geophys Res 79 2783 (1974) 
[15] C G Park J Geophys Res 81 2283 (1976) 
[16] R P Singh, A K Singh and D K Singh J Atmos Solar-Terr Phys 60 495 (1998) 
[17] C G Park, Tech Report no 3454-1, Radtoscience Lab, Stanford University, Stanford, California, 11 17 
(1972) 
[18] P N Khosa, Lalmani and K Knshan Indian J Phys 64 34 (1990) 
[19] Lalmani, A Ahmad and M M Ahmad Planet Space Sci 40 1409 (1992) 
[20] U P Singh and R P Singh J Atmos Solar-Terr Phys 59 1321 (1997) 
[21] R P Singh, D K Singh, A K Singh, D Hamar and J Lichtenberger J Atmos Solar-Terr Phys 61 1081 
(1999) 
[22] R P Singh, R P Patel, A K Singh, D Hamar and J Lichtenberger Pramana J Phys 55 685 (2000) 
[23] R P Singh, Kalpana Singh, Ashok K Singh, D Hamar and J Lichtenberger J Atmos Solar-Terr Phys 68 
710(2006) 
[24] R P Singh, R Singh, Lalmani, D Hamar and J Lichtenberger J Atmos Solar-Terr Phys 66 407 (2004) 
[25] D Hamar, Cs Ferencz, J Lichtenberger, Gy Tarcsai, A J Smith and K H Yearby Radio Sci 27 341 (1992) 
[26] U P Singh, A K Singh, Lalmani, R P Singh and R N Singh Indian J Radio Space Phys 21 246 (1992) 
[27] Cs Ferencz, D Hamar, J Lichtenberger, O E Ferancz, P Stembac and R P Singh Proc URSI Conference 
Maastricht p 1054 (2002) 
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Geophys Res 96 21149(1991) 
[29] Lalmani, R P Singh, R Singh and A Ahmad Earth Moon and Planets 74 7 (1996) 
[30] B Singh and B A P Tantry Ann Geophys 29 561 (1973) 
[31] Y Tanaka and M Hayakawa J Geophys Res 90 3457 (1985)

Estimation of Magnetospheric Electron Densities from Low Latitude Whistlers

Roy, Utpal

Ho, Y K

Computation of Doubly-Excited 1S23l3l′1P° and 1F° States in Beryllium-Like Ions

Chakraborty, B

Pal, R R

l^umJrim. 82(4) 403-4)4(2008) 
A novel high speed fully differential CMOS amplifier 
B Chakraborty and R R Pal* 
Department of Physics and Technophysics, Vidyasagar University, Midnapon? 721 102, West Bengal, India 
E-mail radha_raman_pal^yahoo com 
Received 4 April 2007, accepted 15 January 200S 
Abstract : This paper describes a high speed fully differential CMOS amplifier in which positive feedback is 
employed to improve the operating frequency. By this process the delay time reduces and the speed of operation 
increases An even or odd number of stages can be cross coupled or directly coupled to form ring Voltage 
Controlled Oscillator or Current Controlled Oscillator (VCO/CCO) An improvement of speed of around 167% was 
obtained from circuit simulation (using PSPICE). Here the typical supply voltage requirement is ±2 volt Using this 
amplifier some applications are discussed 
Keywords : Complimentary metal oxide semiconductor (CMOS), voltage controlled oscillator (VCO), current 
controlled oscillator (CCO), ring oscillator, phase locked loop (PLL) 
PACS Nos. : 85.30 -z, 85 30 Tv 
1. Introduction 
Over the last few years there has been a rapid increase in chip complexity which has 
created the need to implement complete analog-digital subsystems on the same 
integrated circuit using the same technology. For this reason, implementation of analog 
functions in CMOS technology has become increasingly important [1,2], 
This paper presents a high speed low voltage CMOS fully differential amplifier. 
The circuit features a positive feedback scheme to improve the speed and to reduce 
the supply voltage requirement of this amplifier (Figure 1). Since the circuit is fully 
differential, push-pull output is possible. To check the improvement in speed an even 
number of such amplifier stages have been cross coupled to form a ring oscillator 
(Figure 2), whose frequency depends on the delay time of each such amplifier stage. 
This ring oscillator also provides a quardrature output which is very much useful in 
various communication systems. 
'Corresponding Author © 2008 IACS 
404 BChakrabortyandRRPai 
In Section 2 detailed Mathematical Operation for decreasing delay time has 
been discussed. The simulated results of the fully differential CMOS amplifier are 
discussed in Section 3. Section 4 includes some applications of this amplifier. 
2. Operation of delay time 
Figure 1 gives the circuit diagram of the fully differential CMOS amplifier using positive 
feedback scheme. By introducing positive feedback the delay produced by each 
amplifier stage is reduced and hence the speed of operation increases [3] The 
frequency of oscillation depends on the number of the inverter stages, the load 
capacitances and the current level. It has been tested by connecting four such 
amplifier stages in series shown in Figure 2 and the outputs of the last stage are 
cross coupled with the inputs of the first stage. 
Figure 1. Circuit diagram of the fully differential CMOS amplifier with positive feedback. 
I 
X1 X2 X3 X4 z~V ? 
Figure 2. Block diagram of a 4-stage ring oscillator. 
A novel high speed fully differential CMOS amplifier 405 
2 1 Calculation of phase factor without positive feedback : 
For mathematical simplicity, we consider a simple CMOS operational amplifier with 
positive feedback shown in Figure 3. An AC small signal equivalent circuit of Figure 
3 is shown in Figure 4. 
o-^[j^ 
<b © 
M2|l f 6 
R, 
M4 
Voo, 
M5 
Figure 3. A simple CMOS operational amplifier. 
The gain of this amplifier (from Figure 4) is 
A , = VRA fl4 + r/-f r2 
where r/ andr2 are the parallel combination of r1f c} and r2t c2; fl3, ft4 are the 
effective drain resistances of MOSFETs M3 and MA respectively. g m l and gm2 are the 
transconductances of M, and M2> r, and r2 are the drain resistances of M1 and A/f2, 
c, and C2 are the drain-source capacitances of W1 and M2 respectively. // is the 
amplification factor. 
So, 
1 + juc^ and rL = 1 + yu;c2r2 
Now, 
406 BChakrabortyandRRPai 
After calculation the phase factor without positive feedback is 
-fa (1 + u;2c|r22) + urlc2 (1 + ufa2^2) off. 
tan ^ = R4 (1 + ^2c12r12)(l + J'clrl) + r, (l + u;2c2r22) + r2 (l + ufa2fi2) 
(see Appendix-i) 
flmlVi © 
© 
v« 4 
Ri 
© 
/////////// 
• • o 
I 9m2V2 
R< 
Figure 4. AC small signal equivalent circuit of Figure 3 
2.2. Calculation of phase factor with positive feedback : 
In the presence of positive feedback resistances, the overall gain of the amplifier will 
be Af = , where (3 is the feedback ratio and 'A is gain of the amplifier without H HA 
positive feedback. 
From Figure 4 we can write, 
B ——'-X—, where R. is the impedance of the next stage, and R,)0. 
Now, 
A = l + BA 
novel high speed fully differential CMOS amplifier 407 
After calculation the phase factor with positive feedback is 
( f l , + f? l ) ( l+u; 2 c| r 2 2 )a ;c l r 1 2 + ( R 1 + fl/)(l 4-u,-2cfr12)u;c2r22 
| / / f l4 (l + w2c2r2)( l-f u;2c2r22)+ft4 (1 W c 2 r 2 ) ( l + u>2c2r22) 
+f i (1 + a;2c|r22) + r2 (1 + a;2Cl2r12)] R, 
+ [f?4 (1 4- u;2cfr2) (1 + u;2C2r22) + r, ( l + u;2c|r22) 
+r2 (1 + uu2c?r?)] fl, (see Appendix-ll) 
If R, = oo i.e. without positive feedback 
tan </>' = tan <f> 
It is evident that tan $' (tan 0, /.e. the phase factor without positive feedback is greater 
than that with positive feedback. Hence with positive feedback, the delay time reduces 
compared to that without positive feedback and the speed of operation increases. 
The same treatment can be applied to the fully differential amplifier circuit of 
Figure 1 with positive feedback and we will get a similar result. That is, with the 
application of positive feedback, delay produced by each inverter of Figure 2 will 
decrease and hence the speed of the inverter will increase. 
3. Simulated results 
The simulated results for percentage speed improvement with positive feedback 
resistance for a particular bias current of 25 \JK is shown in Figure 5. This has been 
tested by connecting four such amplifier stages in series and the outputs of the last 
stage are cross coupled with the inputs of the first stage (Figure 2). The frequency 
of oscillation depends on the number of inverter stages, the load capacitances and the 
current level. This graph indicates that the percentage of frequency improvement is 
maximum for feedback resistance of 33 kfi. For this case an improvement of speed 
of around 167% is obtained. Since each amplifier provides push-pull output, the 
quadrature and multiphase signals can be obtained from such, a ring oscillator. 
Simulated quadrature output waveforms (for feedback resistance of 33 kJ2) are shown 
in Figure 6. These multiphase signals are very useful in communication systems. 
The variation of frequency of oscillation of the above 4-stage ring oscillator with 
bias current for a particular feedback resistance of 47 k(2 is shown in the Figure 7. 
Since the variation is linear over a wide range of current from 25 \xA to 50 \iA% the 
circuit can be very effectively used as current controlled oscillator (CCO) and is 
suitable for Phase Locked Loop (PLL) applications. 
408 B Chakraborty and R R fa 
C 
D 
0 500 100 200 300 400 
Feedback Resistance {Kil) 
Figure 5. Percentage of speed improvement with feedback resistance 
buumv 
0V H 
cnrimW —J 
•ouumv "~i 
w 
L i 
V| 
• 
^ 
' 
f 
! \>* 
-
t 
! " 
' 
, ' 
y 
• 
• 
K I 
V 
4 
1 
^ 1 
" 
*""* 
1 
1 
• 
^ \ 
1 
V 
\ \ 
s i 
k 
^ 
. 1, 
" 
— " 
.~~*. 
" » " • 
' 4 
1 
, 
' 
1 , 
f 
1
 k 
V 
* 
I , 
• i* 
• I 
( 
* 
A j 
^ 1 
F
 i 
f 
-* 
Vi 
" 
65us 70us 
Time 
75us 
Figure 6. Simulated quadrature output waveforms of the 4-stage ring oscillator 
4. Application of the proposed VCO using MOSFETS 
In wireless communication systems, e.g. portable voice, data and messaging systems, 
VCO is an essential part. Frequency synthesizers consisting of VCO, reference 
oscillator, programmable counters are an integral part of transceivers [4], Modern 
communication circuits such as integrated radio paging receivers, QPSK modulators, 
harmonic generators eta need quadrature/multiphase outputs. Synchronized/phase 
locked oscillators are widely used for suppression of noise and interference in an 
incoming signal [5-9]. Phase locked loops provide multiphase clock signals in digital 
circuits [10-14]. Multiphase outputs are also required in coherent PSK reception. 
A novel high speed fully differential CMOS amplifier 409 
220 
215 
~ 210 
I 
o 205 
£ 200 
195 
190 
20 25 30 35 40 45 50 55 60 65 
Bias Current (pA) 
Figure 7. Frequency change with bias current for a feedback resistance of 47 kW 
These multiphase/quadrature outputs may be realized using ring oscillator VCOs as 
described in Figure 2 
4 1 Multiphase/quadrature signal generation -
The extremely accurate phase tracking capabilities of Charge-pump PLLs help us to 
generate multiphase non-overlapping clocks [15-19]. For this case, the VCO should 
comprise of a multistage tapped delay line that is automatically calibrated to a precise 
delay per stage [20], The generation of arbitrary multiphase clocks is possible with 
proper decoding of the signals from the delay line-taps. In many telecommunication 
applications (e.g. synchronous detectors) signals that are in quadrature are needed 
Such quadrature outputs are generated using the 4-stage ring oscillator VCO as 
shown in Figure 2. The signals obtained from the outputs of stages X2 and X4 are 
m phase quadrature and are shown in Figure 6. Note that the frequency of oscillation 
obtained without positive feedback is only 90 KHz at 25 pA, but with positive feedback 
(using 33 kft resistance) it increases to 240 KHz at the same current 
4 2 Zero JF receiver using quadrature signals 
Figure 8 shows a block diagram of the paging receiver. The incoming RF signals are 
mixed in two mixers-one mixer is fed with the in-phase component of a push-pull type 
nng oscillator VCO (used as local oscillator) and the other is fed with its quadrature 
output. The VCO is normally operated at the centre frequency of the received signal. 
At the output of the mixers, two low pass filters are there. These filters have a pass 
410 B Chakraborty and RR fa 
bandwidth of one half the bandwidth of the RF signal spectrum, since information from 
both the high side and low side of the local oscillator is folded over into this frequency 
band. The low frequency output from the mixers, after selection by these filters are 
fully limited in two high gain limiting amplifiers and then treated as digital signals and 
processed by a digital demodulator which consists in its most simple form of a D-type 
flip-flop, as shown in Figure 8. 
'0 ' channel 
OUTPUT 
Y Quadrature 
(a) 
L 
OUTPUT Q » 1 
J L J L 
J 1 I 
M 
OUTPUT Q = 0 
J I 1 L_ 'D* input 
"T 'Clock* input i r 
Figure 8. (a) Block diagram of a zero-IF paging receiver and (b) waveform of the zero-IF paging receiver 
5. Conclusion 
A high frequency fully differential CMOS amplifier with positive feedback has been 
simulated using PSPICE. An even number of such stages have been cross connected 
to form a ring oscillator. Simulated results showed, due to the application of positive 
feedback, a maximum of 167% increase in speed with feedback resistance of 33 kil 
This improved amplifier can operate with a supply voltage of ± 2.0 volts. Current 
tuning characteristics of the ring oscillator is linear over a wide range of current, 
suitable for PLL applications. The presented circuit is highly suitable for VLSI integration, 
where the operating speed can be much higher, depending upon device dimension 
Acknowledgment 
The authors acknowledge Prof. N B Chakraborty, Microelectronics Centre, NT Kharagpur 
for many useful suggestion and advices. 
References 
[1J A H Reyes, E Sanchez-Sinencio and Francisco Duque-Carrillo IEEE Transactions on circuits and system-
II: Analog and Digital signal processing 48 400 (2001) 
411 
[2j p R Gray and R G Meyer IEEE J. Solid State Circuit 17 969 (1982) 
[3] s Sahu, S Chandra, B Chakraborty and R R Pal AMSE Modeling, Measurement and Control 61 1 ((2006) 
[4] B Razavi in Proc. IEEE Custom Integrated Circuit Conference (CICC), Santa Clara, CA 395 (1997) 
[5] Z M Hussain and B Boashash The Time-delay Digital Tanlock Loop : Performance Analysis in Additive 
Gaussion Noise, Journal of the Franklin Institute 339 43 (2002) 
[6] M Badson Automatics 37 1133 (2001) 
[7] C Hycon, J Cornish, K McClellan and J Choma IEEE International Symposium on Circuits Systems 1 233 
(1998) 
[8] R McDonough and A Whalen Detection of Signals in Noise (San Diego • Academic Press) (1995) 
[9] A Hajimiri Noise in Phase locked loops, Southwest Symposium on Mixed Signal Design 1 (2001) 
[10] L Sun and T A Kwasniewski IEEE J. Solid-State Circuits 36 910 (2001) 
[11] Y A Eken and J P Uyemura IEEE J. Solid State Circuits 39 230 (2004) 
[12] C H Heng and B S Song IEEE J. Solid-State Circuits 38 848 (2003) 
[13] J Savoj and B Razavi IEEE J. Solid State Circuits 38 13 (2003) 
[14] MH Kazemeini, M Jamal Deen and S Naseh Proceedings of International Symposium on Computer 
Architecture (ISCA) San Diego, California, USA (2003) 
[15] R L Aguiar and D M Santos 6th IEEE International Conference on Electronics, Circuits and Systems 
(Cyprus :Paphos) (1999) 
[16] Y Woo, Y M Jang and M Y Sung Microelectronics J. 33 245 (2002) 
[17] E J Hernandez and A D Sanchez ELECTRO 2001 283 (2001) 
[18) P M Gardner IEEE Tran. Commun. 28 1849 (1980) 
[19] R Ahola, J Vikla, S Lindfors, J Routama and K Halomen Analog Integrated Circuits and Signal Processing 
18 43(1999) 
[20] S J Lee, B Kim and K Lee IELL J. Solid-State Crcuits 32 289 (1997) 
412 BChakrabortyandRRPai 
Appendix-I 
A = ^ 
"
 R | f l(1-W"l) , r2(1-^C2f2) 
4
 1 + w2c2r? 1 + w2c\rl 
nRA (1 + w^fr,2) (1 + u2c2r22) 
RA (1 -+ u;2cfr,2) (1 + w2cfr22) + r, (1 + w2cfr2) (1 - /^c, r, ) 
+ r z ( n w^fr^Jll-ywCafj) 
/ift4 (1 + uj2c2r2) (1 + w2cfr22) 
RA -f (1 + w2cfr12) (1 + w2c2r22) + r, (l + u^cfr,,2) + r2 (l + w2c12r12) 
- / \ur2c^ (1 + w2c22r22) + urz2c2 (l H- u2c2r2)} 
y* 
where 
X = /if?4 (1 + w2cfrt2) (1 + w2c|r22) 
Y = fl4 (1 + t/cfr,2)(1 + u2c\rl ) + fi (l + u2c22rl) + r2 (l + ^ c f t 2 ) 
and 
Z = {wrfa (14 uj2c\r2) -f u;r2c2 (l + t/cfr,2)} 
So, the phase factor 
tan0 = Z/V 
u>rfa (l -f- o;2c2r22) + urlc2 (l 4- u^cf/f) 
t a n <^>= - - - -
fl4 (1 + uj2c2r2) (1 + J*c\rl) + r, (1 + wzcf r22) + r2 (1 + w2cfr,2) 
Appendix-ll 
(2) 
*'
 =
 T ^ <3) 
4 novel high speed fully differential CMOS amplifier 413 
Y-jZ 
1-+ Y-jZ [flt + flj 
Y-JZ 
(Y-jZ){Ri+R,) + XR, 
[Y-jZ){R,+R,) 
X(ff, + flt) 
(y-yZ)(R1 + R,)+XR, 
X (/?, + /?,) 
VR, + VR, - yZR, - yZR, 4 XR, 
X(f l ,+f l , ) 
( X + V ) R , + VR,-y(R1 + R,)z 
/iff4 (1 + w2C2r2) (1 + u>2C2r22)(/?, -I- R,) 
J|MR4 (l + u;2c2r2)(1 + <Jc\rl) + R4 (l t u>2c2r,2)(l t u>2c2 r22) 
+/, (1 + w2c|/22) + r2 (l + w2^r, !)} R, 
{R4 (1 + w'cfr2) (1 + u;2c|r|) + r, ( n u,2c2r|) + r2 (l + w2^^2)} R, ] 
y f{(l + w2c|r22) wc,r,2 + (1 + u/2c2r,2) uczri) (fl, + R,)] 
+ 
Putting the values of X, V and Z from eq. (2) 
X' 
V'-yZ' (4) 
where 
X' =
 MR4 (1 + «2cf r,2) (1 + w2cf r22) (R, + R,) 
V = |{/xR4 (1 + <A2r2) (l + u,2cfr|) + R4 (l + u,2c2r2) x (l + u,2c2r22) 
+r, (1 + ^ c f r 2 ) + r2 (1 + ^ c f r 2 ) } R, + {fl4 (l + w 2cff f )( l + ^2c2r22) 
+r, (1 + w2cf r22) + r2 (l + u^cfr,2)} R, ]. 
414 BChakrabortyandRRH 
Z' = [|(l + u;2cfr22)a,c1r12 + ( l + w2c,Vi2)<*'C2r22}(f?1 + fl()j 
2" 
The phase factor with positive feedback is tan <j>' = —j 
f ( f l , + R,) (1 + w2c|/22) wc,/-,2 + ( f l , + fl,) (1 + u2c?r?) wc2r22 
* *"*
 =
 ^RA(l + u;2cfri)(l + u;2clri)+RA^+u2cfr,2)^ + u,2cir^ {5> 
-f r, (1 + w2cfr22 ) + r2 (1 + u^cfr,2 )] R, + 
RA (1 + uj2c2r?) (1 + w2cf r22) + rt (1 + w2cf r22 ) + r2 (1 + u;2c,2r12)] 8,

A Novel High Speed Fully Differential CMOS Amplifier

Das, D

Ahmed, G A

Choudhury, A

Indian I Phys. 82 (5), 539-544 (2008) 
Studies on water vapour droplets using a laser based air 
quality monitoring system 
D Das1*, G A Ahmed2 and A Choudhury3 
department of Physics, North Gauhati College, Guwahati-781 031, Assam, India 
department of Physics, Tezpur University, Tezpur-784 028, Assam, India 
3Gauhati University, Guwahati-781 014, Assam, India 
E-mail • dasdihp_3(f/sifycom 
Abstract : This paper is concerned with the design and fabrication of a laser based air quality monitoring 
system combining the design principle of the nephelometer, transmissiometer and a point visibility meter The 
system is tested by investigations on water droplet formation in air having different concentration of different 
gases As such the work involves the theory of extinction and scattering, especially Mie scattering Essentially 
m the system light from a laser source passes through a simulation chamber and the extinction and angular 
scattering of the light is monitored by photo detector arrangement. The signals are digitized and interlaced with 
pc for data recording and processing. Finally a correlation is drawn between the experimental results and the 
theoretical work 
Keywords : Extinction coefficient a , scattering coefficient ft 
PACSNo. • 42.68.kh 
1. Introduction 
Several aspects of environmental pollution are studied all over the world. Our main aim is 
to develop an air quality monitoring system. It is necessary to know the different 
components present in normal air. It is also necessary to find out whether polluting particles 
have entered the air; if so, it will be necessary to quantify the pollutants. So if a relation 
can be found between a certain gas present in air and its characteristic scattering at 
specified angles then it will be possible to infer about the components of gases and their 
quantity from the same measurement. The extinction coefficient o and the scattering 
coefficient /3 are used as a critical parameter for air quality monitoring. By knowing a 
the phenomenon of visibility can be studied because visibility is related to extinction. Also 
Corresponding Author 
© 2008 IACS 
540 D Das, G A Ahmed and A Choudhury 
the instrument yields information about the scattering coefficient /3 as well as the size of 
water droplets [1,2,3,4,5,8] The techniques of measurement used are (i) to compare the 
transmitted intensity of light with the ongmal intensity of light and compute the corresponding 
extinction coefficient and (II) to compute the scattering coefficients by observing the 
scattered intensity from different angles These two are the basic parameters througr 
which the monitoring of air quality is developed and specific observations of water vapour 
in air having varying levels of C0 2 are performed Data have been processed to find out 
specific behaviors of gases towards scattering and absorption with an aim to identify their 
presence Starting from Maxwell's equation and the poynting vector, leading to the theory 
for finding the amplitude scattering matrix and then the stokes parameter for finally 
developing the Mueller matrix for scattering by a particle, as the value of one of the 
elements of the matrix, the element s^ in the first row and first column is experimentally 
determined in our investigations on water droplet formation in air 
The Muller matrix developed is given as 
k2r2 
| Sn Sj2 S,3 S,4 /, 
S21 S22 S2 3 S24 Q, 
$31 $32 $33 $34 Uf 
\ ^41 ° 4 2 ^43 ^44 ) V 
(', 
The 16 scattering matrix elements for a single particle are not all independent only 
seven of them can be independent corresponding to the four moduli | S I , ( j = 1,2 3 4 
and the three differences in phase between the S. Thus there are nine independent relations 
among the StJ The element S r t is related to the measurements made by the air quality 
monitoring system The matrix is the transformation of stokes parameters of the incident 
light to stokes parameters of the scattered light Next Mie theory [6,7] is taken up to 
explain the angular variations of the scattered light by water droplets in air, which is 
investigated by our system and is found to be as follows 
Us 
1 
k2r2 
Sl1 S,2 
S|2 ^11 
0 0 
0 0 
0 0 
0 0 
§33 $34 
_ $34 $33 
u, (2) 
For water droplet state we have l^fl/k2^) S n /, (3) 
The system uses gamma distribution given by N(a) = paYena 
where a is the radius of the particle and A y, r\ are parameters of the distribution related 
to the density of scattering particles Ntot by Ntot =prj~ (y+1)r(y+ 1) Again y and V are 
related to the particle radius a corresponding to the peak of the distribution, the so 
Studies on water vapour droplets using a laser based air quality monitoring system 541 
called modal radius, by ac = yjr] The use of size distribution then leads to the formation 
of the volume scattering coefficient 0(0) for light which is obtained by integrating S n as 
Given by 3 over the size distribution N(a) and is given as, 
P(6) = -^JN(a)Su(6)da (4) 
where P{6) is in units of per steradian per centimeter (sr1crrr1) Thus it is evident from 
3 and 4 that experimental measurements of /sand /, will yield experimental (i(0) values, 
which is used in the system This aspect of the theory is taken advantage of in developing 
a software to simulate, using dummy initial values, theoretical values of (1(0) over a wide 
range of size distributions N(a) and over a range of angles o which may be used in 
drawing a co-relation with the experimental values S^ obtained by investigation on water 
droplets in air [6,7] 
2 System description 
It consists of a He-Ne laser source, some detectors, namely the transmitted light detector, 
the scattered light detector, the reference light detector The scattered light detector detects 
light from seven different angles The light entering these detectors produces photo current 
that is fed through an amplifier to produce the signal carried through one of the three 
channels for input to the Data Acquisition System In the Data Acquisition System, the 
four analog signals are digitized by using ADC 0809 and fed to a pc unit The software 
developed for the pc unit scans the channels and continuously stores the data in the 
hard disc 
3 Extinction coefficient, scattering coefficient, correlation of theory and experimental 
Results 
2o£02 , 
1 8E-02 J 
I 1 6E-02 | 
i 14E02 I 
I 1 2E-02 ] 
' § 1 0E 02 
'
 t 8 0E03 
I 6 0E-03 J 
I 4 OE-03 j 
2 0E03 
0 0E+00 I -
I 3 00E-05 
figure 1. Extinction coefficient a versus water vapour density of air for air having carbon dioxide 
densities of (e) C 0 2 = 6 25x107gm/cc (C02 density of pure air), (f) C0 2 = 2 796x10 6gm/cc, (g) C0 2 = 
4 97x106gm/cc and (h) C 0 2 = 7 14x106gm/cc 
<•) (0 (g) (N 
3 50E05 4 00E05 4 50E-05 5 00E-05( 
water vapour (gm/cc) _ 
542 D Das, G A Ahmed and A Choudhury 
4. Conclusions 
The plots in Figure 1 and Figure 2 shows that there is considerable variation in the 
extinction coefficient as well as volume scattering coefficient of water vapour laden air 
where the C02 levels in air increases beyond the levels normally present in pure air This 
signifies that the trend in which the density of water vapor in the air increases is a 
function of the proportions in which the gaseous constituents of air are present. The plots 
in Figure 3 and Figure 4 represent the expenmentally measured Pav(d) and theoretical 
0 = 22 5° 
QCL 
8 OE-02 
* 6 OE-03 
4 OE-03 
2 0E-02 
0 0E+00 
3 00E-05 3 50E-5 4 00E-05 4 50E-05 
water vapour (gm/cc) 
5 00E-05 
Figure 2. Pav (22 5°) versus water vapour density of air for air having carbon dioxide densities of 
(e) C0 2 = 6 25 x 10~7gm/cc (C02 density of pure air), (f) C0 2 = 2 796 x lO^gm/cc, (g) C0 2 = 4 97x1 o * 
gm/cc and (h) CO,, = 7 14 x lO^gm/cc 
^ 6 0E-01 
t
=CL 
S 4 0E-O1 
3 0E-O1 
2 0E-O1 
1 0E-O1 
0 OE+01 
(7) 
(8) 
- - ( 9 ) 
(10) 
(11) (12) 
157 5 
Figure 3. Experimentally measured Pav(0) and theoretical P(6) versus scattering angle 6 Experimental 
Pav(0) vs 6 graphs are for air having C0 2 density of 6.25 x 10 7gm/cc (C02 density of pure air) and (7) 
water vapour density = 4 20 x 10 -5 gm/cc, (8) water vapour density = 4 40 x 10~5 gm/cc and (9) water 
vapour density = 4 60 x 10~5gm/cc Theoretical P(0) vs 0 graphs are for water vapour with a size 
distribution around (10) modal radius = 0 9um and (11) modal radius = 1.0nm and (12) modal radius -
15 0um 
Studies on water vapour droplets using a laser based air quality monitoring system 543 
0(fj) versus scattering angle. The theoretical pattern corresponding to an aggregate of 
S7, (e) values of water droplets having a particular size distribution N(a), that is 0(0) for 
alt angles 0 • From Figure 3 it can be seen that when air has an C0 2 density of 6.25 x 
iO-7gm/cc and water vapour density of 4.20 x 10-5gm/cc, the experimental flav(G) vs o 
plot (7) corresponds to the plot (12), which is the theoretical P(0) vs o plot for air 
having water droplets with model radius 15.0^m. When the water vapour density is 4.40 x 
1 OE+OO ^ 
9 0E-01 j\ 
8 0E-01 J 
7QE-01 J 
§Boe-oi J 
-
^bOE-01 J 
^ 4 0E CM J 
3 0 F 01 J 
? 0 E 01 -J 
I CIE-01 J 
0 0E <00 4— 
Figure 4. Experimentally measured Pav(0) and theoretical (i(0) versus scattering angle o graphs 
Experimental Pav(0) vs o are for air having C0 2 density of 4.97 x 10 6gm/cc and (p) water vapour 
density = 4 20 x 10~5 gm/cc, (q) water vapour density = 4 40 x 10~5 gm/cc and (r) water vapour density 
= 4 60 x 10 5gm/cc Theoretical [}(()) vs o graphs (s) is for water vapour with a size distribution around 
the modal radius = 30.0jim 
10~5gm/cc, experimental Pav(0) vs 0 plot (8) corresponds to the plot (11), which is the 
theoretical f}(0) vs e plot for air having water droplets with model radius 1.0jnm. 
Finally, when the water vapour density is 4.60 x 10~5gm/cc, experimental (iav(0) vs o 
plot (9) corresponds to the plot (10), which is the theoretical plot for air having water 
droplets with model radius 0.9fim. This shows that while there has been a relatively large 
decrease, that is a change of 14.0^im, in the size of the water droplets when the density 
of water vapour increased from 4.20 x 10~5gm/cc to 4.40 x 10~5gm/cc, for an equal increase 
m water vapour density from 4.40 x 10""5gm/cc to 4.60 x 10~6gm/cc, the size of the water 
droplets changed by only 0.1 urn. It can thus be concluded that when air contains C 0 2 
density equivalent to the density of C0 2 in pure air, with increasing density of water 
vapour in the air, the droplet size of the water vapour will decrease non-linearly. From 
Figure 4 it can be deduced that in air having increased C0 2 densities of 4.97x106gm/cc 
and 7.14 x lO^gm/cc the modal radius of the water vapour droplet is almost constant as 
the density of water vapour in the air increases from 4.20 x 10~5gm/cc to 4.60 x 10*5gm/ 
cc with the modal radius being greater than 30.0 jum, which is again the greatest possible 
modal radius for which theoretical P(0) vs o plot is accurately given. 
(q) • (0 (s) 
544 D Das, G A Ahmed and A Choudhury 
References 
[1] H C Van De Hulst Light scattering by small particles (New York : John Wiley & Sons) (19571 
[2] B S Pntchard and W G Elliot J. Opt Soc. Am 50 191 (1960) 
[3] R E Pasceri and S K Friedlander, J. Atmos. Sci. 22 577 (1965) 
[4] C E Junge J. Atmos. Sci. 26 603 (1969) 
[5] J V Wmstanley and M J Adams Appl. Opt. 14 2151 (1975) 
[6] W J Wiscombe Appl. Opt 19 1505 (1980) 
[7] C F Bohren and D R Huffman Absorption and Scattering of Light by Small Particles (New York 
John Wiley & Sons Inc.) (1983) 
[8] D Das, G A Ahmed, G K D Mazumder and A Choudhury Asian J.Phys 10(3) 323 (2001)

Studies on Water Vapour Droplets Using a Laser Based Air Quality Monitoring System

Bhattacharjee, B

Debnath, B

Sengupta, S

Effect of Collision Geometry on the Multiplicity of Secondary Charged Particles Emitted from 84Kr-AgBr Interactions at 950 MeV/A

Devi, K Nomita

Sarma, H Nandakumar

Kumar, Sanjiv

Indian J. Phys. 82 (6), 747-752 (2008) 
•HI 
Proton induced X-ray emission (PIXE) and proton induced 
Y-ray emission (PIGE) studies of some medicinal plants 
of north east India 
K Nomita Devi*1, H Nandakumar Sarma1 and Sanjiv Kumar 
1
 Department of Physics, Mampur University Canchipur 
Imphal 795 003 Manipur India 
'National Centre for Compositional Characterization of Materials (CCCM) 
Hyderabad 500 062 India 
E mail nomita k(<* rediffmail com 
Abstract Proton induced X-ray emission (PIXE) and proton induced y -ray emission (PIGE) techniques 
were employed for the elemental analysis of twelve different plants traditionally used for medicinal purposes in 
north east India PIXE is a well established ion beam analysis technique for the sensitive and non destructive 
determination of various elements having atomic number greater then eleven present in biological samples while 
PIGE offers a complementary method for the determination of light elements where the sensitivity of PIXE analysis 
is not quite adequate When combined together these analytical techniques provide concentrations of almost all 
elements present in the medicinal plants in quantities above ppm Validity of the techniques was assured by 
analyzing certified plant reference materials (CRMs) A large number of trace elements like Mn, Fe Cu, Zn, Rb, 
Sr, Na and Al are found to be present in the studied plants with variable proportions K, Ca, Mg and P are 
quantified in percentage level while other elements are found to be present in parts per million levels The results 
show that many of these plants contain elements of vital importance for human metabolism and prevention and 
healing of diseases 
Keywords PIXE, PIGE, Medicinal plants, Trace element 
PACS Nos. 78 70 En, 78 70 -g, 23 90 +W 
1. Introduction 
Proton induced X-ray emission (PIXE) and proton induced y-ray emission (PIGE) are 
accelerator based ion beam analysis techniques, capable of simultaneous multi-elemental 
and non-destructive characterization of various complex matrices [1-4]. Medicinal plants 
are a unique type of natural product requiring special considerations due to their potential 
Corresponding Author 
©2008IACS 
748 K Nomita Devi, H Nandakumar Sarma and Sanjiv Kumar 
impact on peoples' health The chemical constituents present in them are a part of the 
physiological function of living flora and hence they are believed to have better compatibility 
with the human body. In addition, medicinal plants contain essential and trace elements 
which qualify them to be used as non-prescription drugs [5] Though it is well known that 
certain trace elements are essential for the healthy growth of plants, the uptake of some 
non-essential elements by these plants can also enhance the medicinal property in specific 
case [6] So the quantitative estimation of various minor and trace element concentration 
are important for determining effectiveness of medicinal plants Further, as certain elements 
at elevated levels are toxic, such an assessment would also be helpful in regulating their 
use 
Manipur, a north-eastern state of India, abounds with rich vegetation, some of which 
are unique and endemic The people of this region have a rich heritage of using plants in 
traditional medicines in the treatment of jaundice, hypertension, asthma and various other 
diseases [7-8]. However, little is known about the trace element distribution in these 
plants In the present work, we determine the major, minor and trace element content of 
twelve medicinal plants commonly used in north-east India by using PIXE and PIGE 
techniques 
2. Experimental 
2 1 Sample preparation 
Fresh samples of different medicinal plants were collected from various areas of Manipur 
The samples were thoroughly washed with distilled water, dried in an oven at 40°C and 
subsequently ground into fine powder The powdered samples were thoroughly mixed with 
high purity graphite powder in the ratio 4:1 by weight. The samples thus obtained were 
further mixed with 200ml of 2-wt % polyvinyl alcohol, a binder, dried under an IR-lamp and 
subsequently pressed into pellet of 18mm diameter and 2mm thickness The thick targets 
of Certified Reference Materials (CRMs) of cabbage (GBW 08504, China), wheat flour 
(NIST-8436) and bovine liver (NIST-1577b) were also prepared in a similar way and irradiated 
for quantification and verification of the results [1] 
2.2. Experimental system and data collection: 
PIXE and PIGE measurements were performed at Surface and Profile Measurement 
Laboratory at CCCM, BARC, Hyderabad using the 3MV Tandetron accelerator. In PIXE 
experiments, a well collimated 2 4 MeV proton beams of diameter 5mm and current 5-
7nA was incident normally on targets placed inside a scattering chamber. The X-rays 
were detected by a planar high purity germanium (HPGe) detector (Eunsys Mesures type 
EGX100-01, Be window thickness 40tim, FWHM of 150 keV at 5.9 keV) placed at 45° to 
the beam axis. A 25\irr\ mylar foil served as the X-ray exit window In PIGE measurements, 
the targets were bombarded with 3 MeV proton beam in the same scattering chamber 
Proton induced X-ray emission (PIXE) and proton induced yray emission (PIGE) etc 749 
and the resulting y-rays were measured with a HPGe detector (Eunsys) of 40 % efficiency 
The vacuum in scattering chamber, pumped by a turbomolecular pump, was about 2 x 
lO^torr. An electron suppressor with - 900 V was placed in front of the samples The 
data were recorded on a PC based MCA 
2.3. Data Analysis : 
The PIXE spectral data were analysed by GUPIX [9] software package which provides 
non-linear fitting of the spectra and converts raw spectral data into elemental concentrations 
For the quantitative PIGE analysis the unknown concentration C , for a specific element 
a in the analyzed sample is calculated by using the following equation [10] 
C =C 
samp a nf a 
Kttni \^o)^uimp I I/, J 
y,,(^K f /(£>2) (1) 
where Y is the yield of the measured y-ray at proton energy E0 and S is the stopping 
power calculated for the sample and the reference material respectively, at proton energy 
This energy corresponds to the proton energy for which the thick target excitation 
"1/2 
yield has obtained half of its value at the incident energy, namely V(£0) - 2Y(Ey) 
Although the stopping power correction in eq (1) should be performed at the mean energy 
E°ft [11 ], the difference in the stopping power evaluation using this value and the 
m 
corresponding one at energy E1/2 has been found to be very small [12 ] 
3. Results and discussion 
Figure 1(a) and 1(b) presents the PIXE and PIGE spectra obtained from the Polygonum 
posumba Bach sample. PIXE spectrum indicates the presence of essential trace elements 
Figure 1. (a) PIXE spectrum (b) PIGE spectrum of Polygonum posumba Bach 
Table 1. Elemental Concentrations of the medicinal plants under study 8 
Plant Samples Elements analysed by PIXE 
K (%) Ca (%) Mn Fe Cu Zn Rb Sr 
Elements analysed by PIGE 
Na Mg (°c) Al P(°o) 
Zanthoxytem acanthopodium 1 98 0 98 50 32 412 
Curcuma domestics 4 84 0 29 24 05 14175 
Oscimum sanctum 3 38 1 76 25 44 384 12 
Hedychium marginatum CB Clarke 2 6 0 57 450 87 295 29 
Acacia famesiana 3 07 0 25 18 14 19015 
Celtis timorensis 0 15 0 14 61 1 51 93 
Menandra benghalensis 167 0 51 127 9 170 07 
Polygonum posumba Bach 1 3 0 86 722 9 112 5 
Cissus javana DC 2 14 1 05 167 265 3 
Zingiber officinale 0 77 0 17 313 42 216 64 
Xylosum longifolia 0 99 1 44 185 06 75 56 
Elaeocarpus ffonbundus Blume 0 24 0 69 65 87 169 79 
4 73 
8 08 
21 99 
1 93 
17 65 
1 81 
9 78 
6 23 
5 
4 47 
4 15 
2 597 
26 4 
45 9 5 28 
49 56 31 96 
155 7 1161 
43 389 19 96 
6 02 
46 47 
66 21 9 
193 01 6 5 
72 53 12 85 
67 77 
13 124 
5 28 
54 48 
109 46 
59 24 
45 93 
46 05 
61 08 
106 77 
301 
338 
6030 
313 
159 
319 
292 
243 
300 
266 
88 
677 
0 65 
0 41 
4 37 
0 30 
0 09 
0 13 
0 42 
0 46 
1 38 
0 92 
0 05 
0 44 
36 
734 
8249 
348 
242 
379 
134 
1191 
640 
60 
108 
374 
0 59 
0 77 
0 68 
011 
0 98 
0 35 
0 59 
0 43 
0 34 
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Proton induced X-ray emission (PIXE) and proton induced y-ray emission (PIGE) etc 751 
nutrient and is important in the breakdown of fats and cholesterol and also helps in the 
nourishment of the nerves and the brain [15] The high content of Mn, Fe and Zn in this 
plant may again support its effective use in the traditional system of medicine by the 
local people of Manipur. The deficiency or excess of a particular trace element can influence 
changes in the functioning, forms, activities of some organs or concentrations of such 
element in the body tissue and fluids can rise above the permissible limit In addition to 
identifying the active secondary metabolites of these medicinal plants, the knowledge of 
their elemental composition is very important in determining their toxicity/safety for use 
4. Conclusion 
PIXE and PIGE techniques have been used in order to determine minor and trace elements 
present in twelve medicinal plant samples The elements Na, Al, Mg, P, K, Ca, Mn, Fe, 
Cu, Zn, Rb and Sr are found to be present in all the twelve medicinal plants in varying 
concentrations. The accuracy and precision of the technique were assured by analyzing 
the Standard Reference materials This preliminary report establishes PIXE and PIGE as 
effective techniques for the multi elemental analysis of plant samples and attempts are 
under progress for future investigation using these techniques. 
Acknowledgments 
The authors are grateful to the authority and supporting staffs of the Surface and Profile 
measurement Laboratory, CCCM, Hyderabad for providing the PIXE facility and the help 
rendered. 
References 
[1] R K Bhamsana Devi, H Nandakumar Sarma J Arunachalam and Sanjiv Kumar Indian J Phys 79 
417 (2005) 
[2] S O Olabanji, O V Makanji, D Ceccato, M C Buoso, A M Haqu, R Cherubim and G Moschmi Biol 
Trace Bern Res 58 (3) 223 (1997) 
[3] K Tantaoui El Araqi, J Guot-Delhalle. I Roelandts, G Weber R Deltour and J Moutschen Environ 
Expt Bot 38 87 (1997) 
[4] N K Sharat Singh, H Nandakumar Sarma, M Sudarshan and A Chakraborty Internal J PIXE 16 21 
(2006) 
[5] R W Hay Bio-Inorganic Chemistry (Chichesten Ellis Horwood Ltd) (1984) 
[6] S Ambe, S Sekido, T Ozaki and I Yamaguchi Appt Radiot Isot 56 473 (2002) 
[7] S C Smha, Medicinal Plants of Manipur (Manipur Association for Science and Society (MASS), 
Manipur Cultural Integration Conference (MCICI) Palace Compound, Imphal) (1996) 
[8J A Jugmdro Vegetable in Manipur (A Ibochouba Singh Mongsangei, Imphal) (1996) 
[9] L J Campbell, L T Hopman, A J Maxwell and Nejedly Zdenek Nucl Instrum Methods B 709 193 
(2000) 
[10J G Deconninck Introduction to Radioanalyttcal Physics (Nuclear Methods Monograph, Budapest) 
(1978) 
752 K Nomita Devi, H Nandakumar Sarma and Sanjiv Kumar 
[11] K Ishi, M Valladon, C S Sastri and J L Debrun Nucl. Instr. Meth. 153 503 (1978) 
[12] A Savidou, X Aslanoglou, T Paradellis and M Pilakouta Nucl. Instr. Meth. B 152 12 (1999) 
[13] S Singh, D K Majumdar and M R Yadav Indian J. Expt. Bio. 34 1212 (1996) 
[14] K Karthikeyan, P Ravichandran and S Govindasamy Oral Oncology 35 112 (1999) 
[15] U C Chaturvedi, Risha Shrivastava and R K Upreti Curr. Sci. 87 1536 (2004)

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