Plasma Heating by a Relativistic Electron Beam. I. Wave Kinetic Equation and Spectral Function
15 Oct 1980-Journal of the Physical Society of Japan (The Physical Society of Japan)-Vol. 49, Iss: 4, pp 1524-1531
TL;DR: In this article, the wave induced by the two-stream instability and Buneman/ion-acoustic wave induce by the return current can coexist and interact to yield a new contribution to plasma heating by relativistic electron beam.
Abstract: A new possibility for plasma heating is proposed and theoretical investigation is performed. Under a suitable experimental condition, the wave induced by the two-stream instability and Buneman/ion-acoustic wave induced by the return current can coexist and interact to yield a new contribution to plasma heating by the relativistic electron beam. The authors assume this is the case and develop the formulation necessary for the analysis of the spectral function of turbulent plasma. Detail of the interaction mechanism and numerical estimation of stopping power are given in the following paper (J. Phys. Soc. Jpn. 49 (1980) 1532).
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TL;DR: In this article, a history of the field and related topics are reviewed, and the momentum space distribution of a relativistic electron beam (REB) is treated, taking into account the kinetic properties of a REB, linear wave dispersion in REB-plasma system is surveyed.
27 citations
TL;DR: In this article, the relativistic transport equations of two electrostatic waves interact nonlinearly with particles, satisfying the resonance condition of ωk−ωk′−(k⊥−k−k ⊥′)vd−n−n∈mωcs/γd2, where v∥ and vd are the parallel and perpendicular velocities of particles, respectively, γd=(1−β2)−1/2, β=vd/c and ωcs is the relatvistic cyclotron
Abstract: Relativistic and nonrelativistic particle acceleration along and across a magnetic field, and the generation of an electric field transverse to the magnetic field, both induced by nonlinear Landau damping (nonlinear wave-particle scattering) of almost perpendicularly propagating electrostatic waves in a relativistic magnetized plasma, are investigated theoretically on the basis of relativistic transport equations. Two electrostatic waves interact nonlinearly with particles, satisfying the resonance condition of ωk−ωk′−(k⊥−k⊥′)vd−(k∥−k∥′)v∥=mωcs/γd2, where v∥ and vd are the parallel and perpendicular velocities of particles, respectively, γd=(1−β2)−1/2, β=vd/c and ωcs is the relativistic cyclotron frequency. The relativistic transport equations show that the electrostatic waves can accelerate particles in the k″ direction (k″=k−k′). Simultaneously, an intense cross-field electric field E0=B0×vd/c is generated via the dynamo effect owing to perpendicular particle drift to satisfy the generalized Ohm’s law, ...
9 citations
TL;DR: In this paper, an anomalous heating was investigated in the system composed of a plasma and a relativistic electron beam (REB) along a uniform external magnetic field, where the wave kinetic equation derived in the preceding paper was applied to the REB-plasma systeun.
Abstract: Anomalous heating is investigated in the system composed of a plasma and a relativistic electron beam (REB) along a uniform external magnetic field. The wave kinetic equation derived in the preceding paper (J. Phys. Soc. Jpn. 49 (1980) 1524) is applied to the REB-plasma systeun. As the mechanism of plasma heating, the wave of the two-stream instability and Buneman or ion-acoustic wave induced by the return current are coupled through the nonlinear wave-particle interaction. High heating rate is obtained from the estimation of the stopping power. The turbulent collision frequency and the perpendicular energy transfer agree with the experimental and numerical results.
4 citations
TL;DR: In this paper, the relativistic Vlasov-Maxwell equations by perturbation theory are derived from the momentum-space diffusion equation and the kinetic wave equation for resonant wave-wave scattering of electromagnetic and electrostatic waves.
Abstract: The momentum-space diffusion equation and the kinetic wave equation for resonant wave-wave scattering of electromagnetic and electrostatic waves in a relativistic magnetized plasma are derived from the relativistic Vlasov-Maxwell equations by perturbation theory. The p-dependent diffusion coefficient and the nonlinear wave-wave coupling coefficient are given in terms of third-order tensors which are amenable to analysis. The transport equations describing energy and momentum transfer between waves and particles are obtained by momentum-space integration of the momentum-space diffusion equation, and are expressed in terms of the nonlinear wave-wave coupling coefficient in the kinetic wave equation. The conservation laws for the total energy and momentum densities of waves and particles are verified from the kinetic wave equation and the transport equations. These equations are very useful for the theoretical analysis of transport phenomena or the acceleration and generation of high-energy or relativistic particles caused by quasi-linear and resonant wave-wave scattering processes.
4 citations
TL;DR: In this article, the authors theoretically analyzed the heating mechanism by waves near the electron cyclotron frequency in the current-sustaining plasma, and showed that the plasma can be heated more effectively by its anisotropy in addition to the ECC resonance.
Abstract: Heating mechanism by waves near the electron cyclotron frequency is theoretically analyzed in the current-sustaining plasma The plasma can be heated more effectively by its anisotropy in addition to the electron cyclotron resonance The heated region becomes broader than that of Maxwellian plasma
2 citations
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TL;DR: In this article, a perturbation theory for solving the Vlasov equation is derived, especially designed to cope with time secularities and nonanalyticity in the expansion parameter (the field strength).
Abstract: A new perturbation theory for solving the Vlasov equation is derived. The theory is especially designed to cope with time secularities and nonanalyticity in the expansion parameter (the field strength). The method is based on the use of a statistical set of exact particle orbits instead of the unperturbed orbits conventionally used in perturbation solutions of the Vlasov equation. A principal result of the theory is a modification of the particle‐wave interaction and a ``broadening'' of the associated resonant denominator (ω − k·v)−1. The nature of the time secularities associated with the streaming modes exp ik·vt is discussed. A simple application to velocity‐space diffusion and trapping and its effect on wave growth is described.
558 citations
TL;DR: In this paper, a simple model for the nonlinear interaction of a low-density monoenergetic electron beam and a relatively cold infinite homogeneous one-dimensional plasma was proposed.
Abstract: Recently, a simple model was proposed for the nonlinear interaction of a low‐density monoenergetic electron beam and a relatively cold infinite homogeneous one‐dimensional plasma. The essential feature of this model is the observation that after several e‐foldings the bandwidth of the growing waves is so narrow that the electrons interact with a very nearly pure sinusoidal field. In terms of this single wave model, a properly scaled solution of the nonlinear beam‐plasma problem which depends analytically on all the basic parameters of the problem (i.e., plasma density, beam density, plasma thermal velocity, and beam drift velocity) is presented. This solution shows that the single wave grows exponentially at the linear growth rate until the beam electrons are trapped. At that time the wave amplitude stops growing and begins to oscillate about a mean value. During the trapping process the beam electrons are bunched in space and a power spectrum of the higher harmonics of the electric field is produced. Both the oscillation in wave amplitude and the power spectrum are given a simple physical interpretation.
384 citations
TL;DR: In this article, the linear stability behavior and anomalous transport properties associated with the lower-hybrid-drift instability are studied assuming flute-like perturbations with k⋅B0=0.
Abstract: The linear stability behavior and anomalous transport properties associated with the lower‐hybrid‐drift instability are studied assuming flute‐like perturbations with k⋅B0=0. Primary emphasis is placed on the low‐drift‐velocity regime with VE≲vThi (here, VE is the cross‐field electron E×B drift velocity), which pertains to the late stages of implosion and the post‐implosion phase of high‐density pinch experiments. Nonlinear estimates of the instantaneous heating rates and rate of momentum transfer are made, and the results are studied numerically to determine the parametric dependence on VE/vThi and the level of turbulent field fluctuation energy EF. It is shown that the lower‐hybrid‐drift instability can result in substantial resistivity and plasma heating for VE≲vThi, as well as for the large‐drift‐velocity regime (VE≳vThi). For example, when Ti/Te≫1 and ω2pe/ω2ce≫1, the bound on anomalous resistivity for VE≲vThi is [nan]max≃4π√π/2(VE/vThi)2 ωLH/ω2ce, where ωLH = (ωciωce)1/2 is the lower‐hybrid frequency. This large value of resistivity is consistent with observations made during the post‐implosion phase of the ZT‐1 experiment.
276 citations
TL;DR: In this article, a novel state of turbulent plasma characterized by small scale phase-space granulations called "clumps" is proposed, where regions of different phase space density are mixed by the fluctuating electric field.
Abstract: A novel state of turbulent plasma characterized by small scale phase‐space granulations called “clumps” is proposed. Clumps are produced when regions of different phase space density are mixed by the fluctuating electric field. They move along ballistic orbits and drive the turbulent field in a manner similar to that in which thermal fluctuations are driven by particle discreteness. In the coherent wave limit the clumps become the familiar trapped particle eddies of a Bernstein‐Green‐Kruskal mode. The turbulent state can exist in the absence of linear instability although it is more likely to occur in a linearly unstable plasma. The spectrum contains a ballistic portion as well as resonances at the wave (collective) frequencies. The discreteness of the clumps produces collision‐like process. For example, the average distribution function satisfies a Fokker‐Planck equation instead of a quasilinear diffusion equation.
236 citations
TL;DR: Theoretical self-consistent relativistic electron beam models are developed in this article, which allow the propagation in excess of the Alfven-Lawson critical current limit for a fully neutralized beam.
Abstract: Theoretical self‐consistent relativistic electron beam models are developed which allow the propagation of relativistic electron fluxes in excess of the Alfven–Lawson critical‐current limit for a fully neutralized beam. Development of a simple, fully relativistic, self‐consistent equilibrium is described which can carry arbitrarily large currents at or near complete electrostatic neutralization. A discussion of a model for magnetic neutralization is presented wherein it is shown that large numbers of electrons from a background plasma are counterstreaming slowly within the beam so that the net current density in the system, and therefore, the magnetic field, is nearly zero. A solution of an initial‐value problem for a beam–plasma system is given which indicates that magnetic neutralization can be expected to occur for plasma densities that are large compared with beam densities. It is found that the application of a strong axial magnetic field to a uniform beam allows propagation regardless of the magnitude of the beam current. Some comparisons are made with recent experimental data.
236 citations