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Fast Ion Non-adiabaticity in Spherical Tokamaks

Description: Transport processes of fast ions in axisymmetric low-aspect-ratio spherical torus (ST) plasmas are investigated, which are induced by the non-conservation of the magnetic moment {mu}. The reason for non-conservation of {mu} of fast ions in ST's is the relatively large adiabaticity parameter epsilon typically exceeding the value 0.1 (epsilon = ratio of ion gyroradius to the gradient scale length of the magnetic field). Both analytical and numerical evaluations of the magnitude of nonadiabatic variations of {mu} are performed. Nonadiabaticity effects are shown to be most significant for fast ions for which the bounce oscillations are in resonance with the gyromotion, i.e., for ions with omega(subscript)B - lomega(subscript)b = 0, where omega(subscript)B and omega(subscript)b represent the bounce-averaged gyrofrequency and the bounce frequency, respectively, and l is an integer. The critical threshold of the adiabaticity parameter, epsilon(subscript)cr, to be exceeded for the transition to stochastic behavior of fast ions in axisymmetric ST's is inspected. Nonadiabatic variations of {mu} are shown to lead to collisionless transformation of trapped orbits into circulating ones and vice versa. For the case of strong nonadiabaticity, epsilon > epsilon(subscript)cr, we assess the transport coefficients describing intense collisionless pitch-angle diffusion, whereas, in the case of weak nonadiabaticity, epsilon > epsilon(subscript)cr, the more substantial coefficients of enhanced collisional radial diffusion and convection of fast ions gyrating resonantly with the bounce oscillations are estimated.
Date: August 1, 2002
Creator: Yavorskij, V.A.; Darrow, D.; Goloborod'ko, V.Ya.; Reznik, S.N.; Holzmueller-Steinacker, U.; Gorelenkov, N. et al.
Partner: UNT Libraries Government Documents Department

A Hamiltonian Model of Dissipative Wave-particle Interactions and the Negative-mass Effect

Description: The effect of radiation friction is included in the Hamiltonian treatment of wave-particle interactions with autoresonant phase-locking, yielding a generalized canonical approach to the problem of dissipative dynamics near a nonlinear resonance. As an example, the negativemass eff ect exhibited by a charged particle in a pump wave and a static magnetic field is studied in the presence of the friction force due to cyclotron radiation. Particles with negative parallel masses m! are shown to transfer their kinetic energy to the pump wave, thus amplifying it. Counterintuitively, such particles also undergo stable dynamics, decreasing their transverse energy monotonically due to cyclotron cooling, whereas some of those with positive m! undergo cyclotron heating instead, extracting energy from the pump wave.
Date: February 7, 2011
Creator: Zhmoginov, A.
Partner: UNT Libraries Government Documents Department

Approximate Integrals of rf-driven Particle Motion in Magnetic Field

Description: For a particle moving in nonuniform magnetic field under the action of an rf wave, ponderomotive effects result from rf-driven oscillations nonlinearly coupled with Larmor rotation. Using Lagrangian and Hamiltonian formalism, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. Those are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the magnetic field. Under the assumption of non-resonant interaction of the particle with the rf field, these integrals represent adiabatic invariants of the particle motion.
Date: April 26, 2004
Creator: Dodin, I.Y. & Fisch, N.J.
Partner: UNT Libraries Government Documents Department

Motion of Charged Particles near Magnetic Field Discontinuities

Description: The motion of charged particles in slowly changing magnetic fields exhibits adiabatic invariance even in the presence of abrupt magnetic discontinuities. Particles near discontinuities in magnetic fields, what we call ''boundary particles'', are constrained to remain near an arbitrarily fractured boundary even as the particle drifts along the discontinuity. A new adiabatic invariant applies to the motion of these particles.
Date: November 7, 2000
Creator: Dodin, I.Y. & Fisch, N.J.
Partner: UNT Libraries Government Documents Department

One-way Ponderomotive Barrier in a Uniform Magnetic Field

Description: The possibility of an asymmetric ponderomotive barrier in a nonuniform dc magnetic field by high-frequency radiation near the cyclotron resonance for selected plasma species was contemplated in Physics of Plasmas 11 (November 2004) 5046-5064. Here we show that a similar one-way barrier, which reflects particles incident from one side while transmitting those incident from the opposite side, can be produced also in a uniform magnetic field, entirely due to inhomogeneity of high-frequency drive.
Date: February 14, 2005
Creator: Dodin, I.Y. & Fisch, N.J.
Partner: UNT Libraries Government Documents Department

Particle dynamics in a wave with variable amplitude. Progress report

Description: Our past research efforts led to the derivation of the adiabatic invariant in spatially varying accelerator structures, to the calculation of the loss of the invariant due to trapping, and to a method for determining transverse invariants using a nonperturbative approach to the Hamilton-Jacobi equation. These research efforts resulted in the training of two graduate students who are now working in the area of accelerator physics.
Date: January 1, 1992
Creator: Cary, J. R.
Partner: UNT Libraries Government Documents Department

Trapped particle dynamics in toroidally rotating plasmas

Description: A detailed single particle orbit analysis is toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first order correction in {rho}{sub pi}(poloidal ion gyroradium)/L{sub v}(scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
Date: June 1, 1992
Creator: Hahm, T. S.
Partner: UNT Libraries Government Documents Department

Nonlinear resonance: Performance report, August 1, 1989--November 30, 1991

Description: This report discusses research concentrated on slowly varying nonlinear oscillatory systems. Some of the topics discussed are; adiabatic invariants and transient resonance in very slowly varying hamiltonians systems; sustained resonance in very slowly varying hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators. (LSP)
Date: December 31, 1991
Creator: Kevorkian, J.
Partner: UNT Libraries Government Documents Department

Particle dynamics in a wave with variable amplitude

Description: Our past research efforts led to the derivation of the adiabatic invariant in spatially varying accelerator structures, to the calculation of the loss of the invariant due to trapping, and to a method for determining transverse invariants using a nonperturbative approach to the Hamilton-Jacobi equation. These research efforts resulted in the training of two graduate students who are now working in the area of accelerator physics.
Date: January 1, 1992
Creator: Cary, J.R.
Partner: UNT Libraries Government Documents Department

Regular and Stochastic Orbits of Ions in a Highly Prolate Field-reversed Configuration

Description: Ion dynamics in a field-reversed configuration (FRC) are explored for a highly elongated device, with emphasis placed on ions having positive canonical angular momentum. Due to angular invariance, the equations of motion are that of a two degree of freedom system with spatial variables rho and xi. As a result of separation of time scales of motion, caused by large elongation, there is a conserved adiabatic invariant, J(sub)rho, which breaks down during the crossing of the phase-space separatrix. For integrable motion, which conserves J(sub)rho, an approximate one-dimensional effective potential was obtained by averaging over the fast radial motion. This averaged potential has the shape of either a double or single symmetric well centered about xi = 0. The condition for the approach to the separatrix and therefore the breakdown of the adiabatic invariance of J(sub)rho is derived and studied under variation of J(sub)rho and conserved angular momentum, pi(sub)phi. Since repeated violation of J(sub)rho results in chaotic motion, this condition can be used to predict whether an ion (or distribution of ions) with given initial conditions will undergo chaotic motion.
Date: October 9, 2003
Creator: Landsman, A.S.; Cohen, S.A. & Glasser, A.H.
Partner: UNT Libraries Government Documents Department

Trapped particle dynamics in toroidally rotating plasmas

Description: A detailed single particle orbit analysis is toroidally rotating plasma yields new analytical formulas for the second adiabatic invariant, the bounce frequency, and the precession frequency up to the first order correction in {rho}{sub pi}(poloidal ion gyroradium)/L{sub v}(scale length of rotation velocity), for toroidal flow values of the order of ion thermal velocity. Toroidal plasma rotation effects on the trapped ion instabilities in tokamaks are investigated in the context of local theory. Toroidal plasma rotation increases both the fraction of trapped particles and their precession drift velocity. Consequently, the growth rate of trapped ion instability increases in both dissipative and collisionless regimes.
Date: June 1, 1992
Creator: Hahm, T.S.
Partner: UNT Libraries Government Documents Department

Nonlinear resonance: Performance report, August 1, 1989--November 30, 1991

Description: This report discusses research concentrated on slowly varying nonlinear oscillatory systems. Some of the topics discussed are; adiabatic invariants and transient resonance in very slowly varying hamiltonians systems; sustained resonance in very slowly varying hamiltonian systems; free-electron lasers with very slow wiggler taper; and bursting oscillators. (LSP)
Date: January 1, 1991
Creator: Kevorkian, J.
Partner: UNT Libraries Government Documents Department

Chaotic dynamics in accelerator physics. [Dept. of Astrophysical, Planetary, and Atmospheric Sciences, Univ. of Colorado, Boulder]

Description: Substantial progress was in several areas of accelerator dynamics. For developing understanding of longitudinal adiabatic dynamics, and for creating efficiency enhancements of recirculating free-electron lasers, was substantially completed. A computer code for analyzing the critical KAM tori that bound the dynamic aperture in circular machines was developed. Studies of modes that arise due to the interaction of coating beams with a narrow-spectrum impedance have begun. During this research educational and research ties with the accelerator community at large have been strengthened.
Date: November 30, 1992
Creator: Cary, J.R.
Partner: UNT Libraries Government Documents Department

Stochasticity and superadiabaticity in radiofrequency plasma heating

Description: In a plasma subject to radiofrequency fields, it is only the resonant particles - comprising just a minor portion of the total velocity distribution - which are strongly affected. Under near-fusion conditions, thermalization by Coulomb collisions is slow, and noncollisional stochasticity can play an important role in reshaping f(v). It is found that the common rf interactions, including Landau, cyclotron and transit-time damping, can be fitted in a unified manner by a simple two-step one-parameter (epsilon) mapping which can display collision-free stochastic or adiabatic (also called superadiabatic) behavior, depending on the choice of epsilon. The effect on the evolution of the space averaged f (x,v,t) is reasonably well described by a pseudo-stochastic diffusion function, D/sub PS/(v,epsilon) which is the quasilinear diffusion coefficient but with appropriate widening of the delta-function spikes. Coulomb collisions, leading to D/sub Coul/(v) which may be added and directly compared to D/sub PS/(v,epsilon), are introduced by Langevin terms in the mapping equations.
Date: April 1, 1979
Creator: Stix, T.H.
Partner: UNT Libraries Government Documents Department

Motion of a charged particle in a nearly axisymmetric magnetic field

Description: The motion of a charged particle in a static magnetic field is studied by means of repeated canonical transformations of a Hamiltonian system. Adiabatic invariants are generated based on the assumption that the particle larmor radius is small compared with the characteristic distance over which the magnetic field varies. Unlike many earlier treatments the transformations presented here preserve the axisymmetry of the dynamics when the magnetic field is axisymmetric. It is assumed that the magnetic field consists of a small nonaxisymmetric part plus the axisymmetric toroidal and poloidal parts. After the introduction of the magnetic moment adiabatic invariant the motion of the guiding center is studied. The results depend sensitively on the ratio of the poloidal magnetic field to the total magnetic field. In some cases a second adiabatic invariant exists and direct inferences concerning long time particle drifts are possible. In one case where a second adiabatic invariant fails to exist, long term drifts are studied by conventional perturbation expansions. At some points resonance or lack of resonance phenomena appear and determine the drift effects.
Date: November 1, 1980
Creator: Weitzner, H
Partner: UNT Libraries Government Documents Department

Adiabatic invariants for field-reversed configurations

Description: Field reversed configurations (FRCs) are characterized by azimuthal symmetry, so two exact constants of the particle motion are the total particle energy E and the canonical angular momentum P/sub theta/. For many purposes it is desirable to construct a third (diabatic) constant of the motion if this is possible. It is shown that for parameters characteristic of current FRCs that the magnetic moment ..mu.. is a poor adiabatic invariant, while the radial action J is conserved rather well.
Date: January 1, 1982
Creator: Schwarzmeier, J.L.; Lewis, H.R. & Seyler, C.E.
Partner: UNT Libraries Government Documents Department

Stochasticity, superadiabaticity, and the theory of adiabatic invariants and guiding center motion

Description: The theory of adiabatic invariants is discussed within the modern framework of symplectic Hamiltonian dynamics. The distinctions between exact, adiabatic, and superadiabatic invariants are clarified. The intimate connection between adiabatic (as opposed to exact) invariance and resonant interactions between motions on disparate time scales is elucidated. For the important case of charged particle motion in a strong magnetic field, resonances between gyration, bounce motion, and an external sinusoidal perturbation are described explicitly by introducing a time-dependent symplectic formulation of the guiding center motion. Destruction of invariance is discussed for quite general situations of physical interest, including the case of a trapped particle in a tokamak.
Date: July 1, 1981
Creator: Dubin, D.H.E. & Krommes, J.A.
Partner: UNT Libraries Government Documents Department