The dissipation induced by coulomb-collisional scattering provides an irreducible minimum, and thus a useful standard for comparison, for transport processes in a hot, magnetically confined plasma. The kinetic description of this dissipation is provided by an equation of the Fokker-Planck form. As in the standard transport theory for a neutral gas, approximate solution of the Fokker-Planck equation permits the calculation of transport coefficients, which linearly relate the fluxes of particles, energy, and electric charge, to the density and temperature gradients, and to the electric field. The transport relations are useful in studying the confinement properties of present and future experimental devices for research in controlled thermonuclear fusion. The transport theory for a magnetized plasma (in which the Larmor radius is much smaller than gradient scale lengths describing the plasma fluid) departs from the theory for a neutral gas in several fundamental ways. Thus, transport coefficients for a magnetized plasma can be calculated even when the collisional mean free path is much longer than the gradient scale length (as would pertain in thermonuclear regimes). Such transport coefficients are generally nonlocal, being defined in terms of averages over surfaces with macroscopic dimensions. Furthermore, when the mean free path is long, the magnetized-plasma transport coefficients depend crucially upon the magnetic field geometry, the effects of which must be treated at the kinetic level of the Fokker-Planck equation. The results display several novel couplings between collisional dissipation and the electromagnetic field. The present review of magnetized-plasma transport theory is intended to be as widely accessible as possible. Thus the relevant features of magnetic confinement in closed (toroidal) systems, and of charged particles in spatially varying fields, are derived, at least in outline, from first principles. Although consideration is given to "classical" transport in which most field geometric effects are omitted, major emphasis is placed on the "neoclassical" theory which has been developed over the last decade. Neoclassical transport coefficients are specifically relevant to a magnetically confined plasma, rather than to just a magnetized plasma; their unusual features, such as nonlocality and geometry dependence, become particularly important in the high temperature regime of proposed thermonuclear reactors. The area of neoclassical theory which seems most complete---its application to axisymmetric tokamak-type confinement systems---is correspondingly stressed.

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Theory of plasma transport in toroidal confinement systems

An overview is given of the physics issues relevant to the plasma wakefield accelerator, the plasma beat-wave accelerator, the laser wakefield accelerator, including the self-modulated regime, and wakefield accelerators driven by multiple electron or laser pulses. Basic properties of linear and nonlinear plasma waves are discussed, as well as the trapping and acceleration of electrons in the plasma wave. Formulas are presented for the accelerating field and the energy gain in the various accelerator configurations. The propagation of the drive electron or laser beams is discussed, including limitations imposed by key instabilities and methods for optically guiding laser pulses. Recent experimental results are summarized.

Overview of plasma-based accelerator concepts

We show that the relativistic two-stream instability can naturally generate strong magnetic fields with 10-5-10-1 of the equipartition energy density, in the collisionless shocks of gamma-ray burst (GRB) sources. The generated fields are parallel to the shock front and fluctuate on the very short scale of the plasma skin depth. The synchrotron radiation emitted from the limb-brightened source image is linearly polarized in the radial direction relative to the source center. Although the net polarization vanishes under circular symmetry, GRB sources should exhibit polarization scintillations as their radio afterglow radiation gets scattered by the Galactic interstellar medium. Detection of polarization scintillations could therefore test the above mechanism for magnetic field generation.

/pdf/generation-of-magnetic-fields-in-the-relativistic-shock-of-3onlkm3k8p.pdf

Generation of Magnetic Fields in the Relativistic Shock of Gamma-Ray Burst Sources

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

A review of measurements of microscopic fluctuations and theories of turbulence and anomalous transport for tokamaks is given, and some comparisons between theory and experiment are presented. The results of the measurements indicate that all tokamaks have rather similar, broadband, incoherent microscopic fluctuations. Such fluctuations have been measured in the density, potential, electric field, and magnetic field. In the edge regions of three tokamaks, the particle transport caused by the turbulent electric field fluctuations has been measured directly. Although tokamak microturbulence has been studied extensively, neither its source nor its role in anomalous energy transport is yet understood. The incoherent, turbulent nature of the fluctuations has made it difficult to understand them theoretically. Recently, however, significant theoretical progress has been made in several areas including non-linear models of drift wave turbulence and transport, models of anomalous electron thermal conduction by stochastic magnetic field fluctuations, and non-linear models of localized resistive-MHD instabilities.

https://iopscience.iop.org/article/10.1088/0029-5515/25/5/004/pdf

Measurements of microturbulence in tokamaks and comparisons with theories of turbulence and anomalous transport

We analyze the effects of (i) the nonlinearity of the large-amplitude plasma wave, and (ii) the inhomogeneity of the plasma, on the excitation of the plasma wave by beating two laser beams.

Excitation of Plasma Waves by Two Laser Beams

It is shown that shear Alfv\'en waves can be destabilized by resonance with high-energy "beam" ions near the magnetic axis in a tokamak, if the beam is radially nonuniform.

/pdf/excitation-of-alfven-waves-by-high-energy-ions-in-a-tokamak-2qgg5cldnf.pdf

Excitation of Alfven waves by high-energy ions in a tokamak

Plasma diffusion in a toroidal stellarator.

It is shown that trapping-electron--induced scattering can be dominant over nonlinear ion Landau damping in the saturation of short-wavelength, dispersive, trapped-electron instabilities in tokamaks. Trapped-electron-induced scattering transfers the wave energy to shorter wavelengths, where it can be dissipated by ion viscosity.

Nonlinear saturation of the dissipative trapped-electron instability

/pdf/excitation-of-alfven-waves-by-high-energy-ions-in-a-tokamak-96jgnsfwk8.pdf

M. N. Rosenbluth

Papers

Excitation of Plasma Waves by Two Laser Beams

Excitation of Alfven waves by high-energy ions in a tokamak

Plasma diffusion in a toroidal stellarator.

Nonlinear saturation of the dissipative trapped-electron instability

Excitation of Alfven waves by high-energy ions in a tokamak