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Theoretical study and design of a CARM type millimeter wave source
Full text linkIn Nuclear Fusion external heating sources play a role of paramount relevance for the twofold role of plasma heating and instability suppression. The effectiveness of Electron Cyclotron (EC) waves in Tokamaks have been experimentally demonstrated since the early 80’s of the last century (see e. g. the pioneering work by R.M. Gilgenbach et al., 1980). Nowadays EC systems plays a pivotal role in magnetic fusion devices and their need in future experimental reactors is out of doubt. The physical reasons underlying these choices stems from the fact that electron cyclotron radiation can be coupled effectively to the plasma, producing a localized and controlled energy deposition. Within this framework an important tool has been provided by the electron cyclotron masers (ECM) sources, namely gyrotronlike device, extensively used because able to provide sufficiently large power in the millimeter and sub-millimeter region. The gyrotrons provide the most mature and reliable technology in the field of millimeter-wave tubes, their use is however hampered by the fact that they meet some difficulty of operation (in terms of delivered power and efficiency) in the spectral range above 200 GHz.
The possibility of exploiting different generators of powerful millimeter-wave coherent radiation has therefore been suggested. In this context a research and development program has been undertaken at ENEA Frascati Center, aimed at realizing a microwave tube based on a Cyclotron Auto-Resonance Maser (CARM) oscillator, characterized by a high value of the Doppler up-shift interaction allowing a consistent reduction of the static magnetic field in the interaction cavity and enhanced efficiency with a moderately relativistic beam due to the auto resonance mechanism. The price to be paid is the necessity of exploiting high quality electron beams, with velocity spread below 0.5%, in order to ensure appropriate mode selection, enough gain to oscillate and adequate beam-wave power transfer with the required efficiency. The low beam quality has been the main element that has affecting the performances of the first CARM experiments on the eve of the last century. Most of the them used already existing high-voltage accelerators producing electron beams with currents of several kA. They were powered by modulators having non-appropriate waveform with respect to flat-top ripple. The beam was emitted from a cold cathode and then blasted toward the small aperture, used either to scratch out the largest part of the beam and as an emittance filter. This mechanism never succeeded to deliver a beam with appropriate characteristics. Even though the data relevant to the beam qualities are rather insufficient, serious doubts can be raised on the reliability of such drivers for CARM operation.
The research line associated with the present Ph.D. thesis, developed at ENEA with the CARM project team, has gone through different phases, the first of which has been the understanding of the physical mechanisms underlying the operation of the different devices (Gyrotron, FEL, CARM, Gyro-Backward. . . ). A significant part of the thesis has been devoted to the design of the various components of the CARM device, including the cathode, the principal magnet and the radiation confining cavity. Most of the design effort has been devoted to the production of a beam with suited characteristic for the CARM operation. Successively, particular care has been devoted in putting in evidence the relative pro’s and con’s and noticeable efforts has been devoted to the understanding of the factors which have limited the CARM efficiency in the past experiments.
In chapter 1 we review the relevant issues to the thermonuclear fusion as a clean solution for the world energy demand putting in evidence the requirements for a commercial power fusion plant. In particular the studies, undertaken under auspices of the European Fusion Development Agreement (EFDA) for a different configuration of a DEMOnstration fusion reactor, get out the importance of the efficiency for the Heating and Current Drive (H&CD) systems. We report a short description of the physical mechanism governing the fusion reaction. We discussed the role played by the plasma instabilities in a Tokamak plant and the necessity of their suppression or control. We put therefore in evidence the necessity of additional H&CD devices in Tokamak plants and analyze the required characteristics in terms of frequency and power.
In chapter 2 we describe the design of the ENEA CARM facility. We start with the analysis of a thermionic gun and perform accurate simulation determine the conditions for the generation of a high quality beam, in terms of the longitudinal velocity spread. The simulation are benchmarked with an analytical modeling of the beam transport by means of the generalization of the Courant-Snyder formalism
which simplifies the beam transport design for this device, demanding for an accurate control of the beam transverse dimension. The forthcoming chapter 3 contains a thorough analysis of CARM interaction,
carried out using previous theoretical formulation providing the coupled beam-wave evolution equations. The theory is then confronted with that of U-FEL systems. The results of this efforts is that of providing a set of semi-analytical formulae useful for a quick design of the device. The relevant reliability has been benchmarked using the home-made code GRAAL and tested for a variety of study cases. Furthermore, a “universal” scaling formula describing the CARM performance embedding inhomogeneous broadening effects and the beam current, as it happens in the case of U-FEL, has been derived for monitoring the accuracy and for diagnosing the calculations during the numerical experiments.
The concluding chapter 4 deals with the CARM oscillator configuration. It contains the description of the system, the evaluation of the gain and saturation mechanism and the design of the radiation confining cavity with particular reference to the relevant optimization of the suppression of the spurious modes
The Humbert-Bessel Functions, Stirling Numbers and Probability Distributions in Coincidence Problems
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Rete capillare, cancro e legge di Kleiber
Full text linkLo studio dell’evoluzione dei complessi biologici ha beneficiato dell’utilizzo di leggi di scala che coinvolgono relazioni tra massa e fabbisogno energetico. L’uso congiunto di modelli, quali le leggi di Kleiber e di Murray, ha aperto nuove possibilità per l’analisi quantitativa della crescita delle masse
cancerose, della relativa vascolarizzazione ed evoluzione metastatica. In questo articolo si descrivono i risultati essenziali delle ricerche in tali campi e si esaminano come tali studi possano avere un impatto efficace sulla pratica clinic
On an Umbral Point of View of the Gaussian and Gaussian-like Functions
Full text linkThe theory of Gaussian functions is reformulated using an umbral point of view. The symbolic method we adopt here allows an interpretation of the Gaussian in terms of a Lorentzian image function. The formalism also suggests the introduction of a new point of view of trigonometry, opening a new interpretation of the associated special functions. The Erfi ( x ) , is, for example, interpreted as the “sine” of the Gaussian trigonometry. The possibilities offered by the Umbral restyling proposed here are noticeable and offered by the formalism itself. We mention the link between higher-order Gaussian trigonometric functions, Hermite polynomials, and the possibility of introducing new forms of distributions with longer tails than the ordinary Gaussians. The possibility of framing the theoretical content of the present article within a redefinition of the hypergeometric function is eventually discussed
Free Electron Laser High Gain Equation and Harmonic Generation
No full textThe FEL integral equation is reviewed here and is studied under different contexts, accounting for diverse physical regimes. We include higher order harmonics and saturation effects, and explain the origin of scaling relations, widely exploited to describe either FEL dynamics or nonnlinear harmonic generation
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