Miklos Porkolab

Upper‐hybrid solitons and oscillating‐two‐stream instabilities

A warm two‐fluid theory of soliton formation near the upper‐hybrid frequency is developed. Several forms of the nonlinear Schrodinger equation are obtained, depending on whether the electric field is completely perpendicular to the dc magnetic field or whether it has an additional small component parallel to the magnetic field. For the perpendicular case, the character of the soliton depends on its scale length, L, and on β. For low β, when L<c/ωpe, stationary envelope and hole solitons are found, whereas in the limit L≳c/ωpi the super‐Alvenic solitons described magnetohydromagnetically by Kaufman and Stenflo are obtained. However, the case E∥≠0 may be of more interest, since it couples the pump to the excited waves more efficiently. In the limit of linearization about an infinite wavelength pump, the nonlinear Schrodinger equations yield purely growing (oscillating‐two‐stream) instabilities in both cases.

Theory of parametric instability near the lower‐hybrid frequency

The dispersion relation for parametric instabilities near the lower‐hybrid frequency is derived and analyzed. It is found that for propagation angles cos2θ(mi/me) < 1 resonant decay into ion acoustic (ion‐cyclotron) waves does not occur; rather, decay into nonresonant quasi‐ion modes and lower‐hybrid waves occurs. The driving mechanism for this instability is shown to be analogous to nonlinear Landau damping in perturbation theory. The large amplitude dispersion relation is analyzed numerically for a number of typical experimental regimes, and growth rates and thresholds are obtained for both the purely growing mode and the newly found quasi‐ion modes.

Parametric instabilities due to lower‐hybrid radio frequency heating of tokamak plasmas

The linear theory of parametric instabilities relevant to radiofrequency heating near the lower‐hybrid frequency of tokamak‐type plasmas is presented. The dispersion relations are analyzed numerically to all orders of the ion Larmor radius. The complete range of unstable spectra is obtained for 1<ω0/ωlh<5, for both deuterium and hydrogen plasmas. As the pump wave propagates from the edge of the plasma toward its interior, the transition from resonant decay to decay into quasi‐modes is demonstrated. The effects of inhomogeneities upon the threshold for parametric decay, such as density gradients, finite pump width, and magnetic shear, are obtained. The relevance of these results to recent tokamak experiments is discussed briefly.

Propagation and mode conversion of lower-hybrid waves generated by a finite source

The propagation of electrostatic plasma waves, and their subsequent conversion into hot plasma waves at the lower hybrid frequency is calculated for realistic density profiles and finite rf sources in a slab geometry. A finite length slow wave source having a potential distribution phi ~ cosk0z is found to generate spatial oscillations having a well-defined wavelength. These oscillations are confined to regions bounded by conical curves originating at the ends of the source. The axial distance of rf energy propagation to the lower hybrid layer is found to be greater than the radial distance of propagation by a factor of the order (mi/me)1/2. The conversion at the lower hybrid layer of the electrostatic cold plasma waves excited by a finite source into propagating hot plasma waves is calculated. It is shown that collisional damping at the lower hybrid layer may predominate over mode conversion even for relatively low collision frequencies.

Bremsstrahlung and Kα fluorescence measurements for inferring conversion efficiencies into fast ignition relevant hot electrons

The Bremsstrahlung and K-shell emission from 1×1×1 mm3 planar targets irradiated by a short-pulse 3×1018–8×1019 W/cm2 laser were measured. The Bremsstrahlung was measured using a filter stack spectrometer with spectral discrimination up to 500 keV. K-shell emission was measured using a single photon counting charge coupled device. From Monte Carlo modeling of the target emission, conversion efficiencies into 1–3 MeV electrons of 3%–12%, representing 20%–40% total conversion efficiencies, were inferred for intensities up to 8×1019 W/cm2. Comparisons to scaling laws using synthetic energy spectra generated from the intensity distribution of the focal spot imply slope temperatures less than the ponderomotive potential of the laser. Resistive transport effects may result in potentials of a few hundred kV in the first few tens of microns in the target. This would lead to higher total conversion efficiencies than inferred from Monte Carlo modeling but lower conversion efficiencies into 1–3 MeV electrons.

Instabilities and induced scattering due to nonlinear Landau damping of longitudinal plasma waves in a magnetic field

The matrix elements for nonlinear wave‐particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov‐Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k⊥≫k‖, the symmetry relations for mode‐mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss‐cone modes. In additi...

Experimental studies of lower hybrid wave propagation

Experimental measurements of the dispersion and damping of externally excited lower hybrid waves are presented. A multiple-ring slow-wave antenna, having 2

Parametric instabilities in a magnetic field and possible applications to heating of plasmas

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Observation of the parametric decay instability during electron cyclotron resonance heating on the Versator II tokamak

/k/sub z/ = 23 cm, is used to excite these waves in the Princeton L3 or L4 linear devices (B = 0.5 -- 2.8 kG uniform to +- 1 percent for 1.6 m, n approximately 10

Studies of turbulence and transport in Alcator C-Mod H-mode plasmas with phase contrast imaging and comparisons with GYRO

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