A. Bers

The cusp map in the complex-frequency plane for absolute instabilities

It is well known that absolute instabilities can be located by prescribed mappings from the complex‐frequency plane to the wavenumber plane through the dispersion relation D(ω,k)=0. However, in many systems of physical interest the dispersion relation is polynomial in ω while transcendental in k, and the implementation of this mapping procedure is particularly difficult. If one maps consecutive deformations of the Fourier integral path (originally along the real k axis) into the ω plane, points having (∂D/∂k)=0 are readily detected by the distinctive feature of their local maps. It is shown that a simple topological relationship between these points and the image of the real k axis determines the stability characteristics of the system, without mapping from the ω plane back into the k‐plane.

Surface state memory in surface acoustoelectric correlator

We show that surface acoustic signals can be stored in and read from electron traps at the surface of a semiconductor that is adjacent to the piezoelectric on which the surface wave propagates. The observed memory action is explained by the large‐signal dynamics of the charging and discharging of the traps near a slightly depleted surface. The storage of the signal is accomplished by creating a zero‐frequency k pattern which fills the traps. The reading of the signal can be done by either correlation or convolution with another surface acoustic signal. This correlation device with internal memory does not require precise signal timing, operates with all signals at the same frequency, and does not require external time inversion of the reference signal.

Theory of mode-conversion in weakly inhomogeneous plasma

The theory of pair‐wise coupled modes excited at a real frequency ω in a weakly nonuniform plasma (coordinate x) is developed on the basis of general local dispersion relations D(k,z) = 0 (such as from the Vlasov equation), which define a many‐valued mapping of the real axis x = Rez onto the complex plane of the wavenumber k. Mode coupling, by definition, is the analytical continuation of the branch of the mapping and only occurs at the branch points. This requires that the z plane be cut along contours Cb given by D(kc,Cb) = 0, ∂D(kc,z)/∂k = 0, where z traces a contour passing through the branch points. The coupled modes can be analyzed by expanding the dispersion relation to second order in k around the saddle points and along the lines kc(x), yielding a system of dispersion relations corresponding to unambiguous second‐order differential equations, guaranteed to have the right turning point behavior.

Mode conversion of fast Alfven waves at the ion-ion hybrid resonance

Substantial radio‐frequency power in the ion‐cyclotron range of frequencies can be effectively coupled to a tokamak plasma from poloidal current strap antennas at the plasma edge. If there exists an ion–ion hybrid resonance inside the plasma, then some of the power from the antenna, delivered into the plasma by fast Alfven waves, can be mode converted to ion‐Bernstein waves. In tokamak confinement fields the mode‐converted ion‐Bernstein waves can damp effectively and locally on electrons [A. K. Ram and A. Bers, Phys. Fluids B 3, 1059 (1991)]. The usual mode‐conversion analysis that studies the propagation of fast Alfven waves in the immediate vicinity of the ion–ion hybrid resonance is extended to include the propagation and reflection of the fast Alfven waves on the high magnetic‐field side of the ion–ion hybrid resonance. It is shown that there exist plasma conditions for which the entire fast Alfven wave power incident on the ion–ion hybrid resonance can be converted to ion‐Bernstein waves. In this ext...

Surface mobility measurement using acoustic surface waves

The sheet mobility of accumulated electrons on silicon has been determined by measuring the acoustoelectric current which accompanies the interaction between these electrons and piezoelectric surface waves on LiNbO3. The advantages of this method are (a) it is a direct mobility measurement (not requiring a knowledge of density), (b) the effect of surface states may be made negligible, (c) it is a zero‐average applied‐field measurement, (d) both majority‐ and minority‐carrier mobilities may be measured on the same sample. By using high‐resistivity (30 000 Ω cm) silicon with an accumulated surface, the sheet density was varied from 1.5×1010 to 5×1011 cm−2. Over this range the mobility was determined to vary from 1100 to 450 cm2/V sec, respectively.

Ion dynamics in multiple electrostatic waves in a magnetized plasma. I. Coherent acceleration

A new phenomenon of coherent acceleration of ions by a discrete spectrum of electrostatic waves propagating perpendicularly to a uniform magnetic field is described. It allows the energization of ions whose initial energies correspond to a region of phase space that is below the chaotic domain. The ion orbits below the chaotic domain are described very accurately using a perturbation analysis to second order in the wave amplitudes. This analysis shows that the coherent acceleration takes place only when the wave spectrum contains at least two waves whose frequencies are separated by an amount close to an integer multiple of the cyclotron frequency. The way the ion energization depends on the wave numbers and wave amplitudes is also presented in detail using the results of the perturbation analysis.

A ONE-DIMENSIONAL MODEL FOR LOWER HYBRID CURRENT DRIVE INCLUDING PERPENDICULAR DYNAMICS**

The two‐dimensional (velocity space) Fokker–Planck equation for lower‐hybrid current drive is approximated by its perpendicular moments hierarchy closed in the second moment equation. The closure is derived on the basis of a distribution function composed of a central thermal Maxwellian plus a perpendicularly broadened distribution of fast particles that are diffused into, and pitch‐angle scattered out of, the quasilinear plateau region. The resulting one‐dimensional model reproduces the relevant features of the solutions obtained from numerically integrating the two‐dimensional Fokker–Planck equation. An analytic estimate of the perpendicular temperature on the plateau and the plateau height as a function of spectrum width and position is presented. Also predicted are the current density generated and its figure of merit (the current density per unit power density dissipated).

Emission of electron Bernstein waves in plasmas

In previous publications [A. K. Ram and S. D. Schultz, Phys. Plasmas 7, 4084 (2000); A. Bers, A. K. Ram, and S. D. Schultz, in Proceedings of the Second Europhysics Topical Conference on RF Heating and Current Drive of Fusion Devices, edited by J. Jacquinot, G. Van Oost, and R. R. Weynants (European Physical Society, Petit-Lancy, 1998), Vol. 22A, pp. 237–240] it has been shown that, in overdense plasmas of the type encountered in spherical tori, electron Bernstein waves can be excited in a plasma by mode conversion of either an externally launched X mode or an O mode. The electron Bernstein waves are strongly absorbed by electrons in the region where the wave frequency matches the Doppler broadened electron cyclotron resonance frequency or its harmonics. The strong absorption also implies that electron Bernstein waves are emitted by a thermal plasma. These waves can then mode convert to the X mode and to the O mode and be observed external to the plasma. In this paper an approximate kinetic model describing the coupling between the X mode, the O mode, and the electron Bernstein waves is derived. This model is used to study the mode conversion properties of electron Bernstein wave emission from the plasma interior. It is shown, analytically and numerically, that the energy flow conversion efficiencies of the electron Bernstein wave to the X mode and to the O mode are the same as the energy flow conversion efficiency of the X mode to electron Bernstein waves and of the O mode to the electron Bernstein waves, respectively. This has important experimental consequences when designing experiments to heat overdense plasmas by electron Bernstein waves.

Ion dynamics in multiple electrostatic waves in a magnetized plasma. II. Enhancement of the acceleration

The maximal energy an ion can gain from a discrete spectrum of electrostatic waves propagating perpendicularly to a uniform magnetic field is investigated. In the case when the wave spectrum contains at least two on-resonance waves, the ion is shown to reach energies which are much higher than in the case of one wave. When the ion energization is enhanced, even when the ion motion is not coherent, the ion orbit remains close to orbits found from a first order perturbation analysis. This implies that, unlike in the case of a single wave, the ion can reach high energies regardless of how small the wave amplitudes are. The dependence of the ion energization on the wave spectrum characteristics is described in great detail by deriving the extent, in action, of the first order orbits, and the way these orbits may connect.

A theory of fast‐wave absorption, transmission, and reflection in the ion cyclotron range of frequencies

A second‐order differential equation for the fast wave propagating in a hot, two‐ion species plasma is obtained. This second‐order approximation is obtained unambiguously and allows the wave amplitude to be identified with one of the electric field components. The approximation is based on replacing the coupling to the ion‐Bernstein wave by a localized perturbation of the fast wave. For the case of perpendicular propagation, the second‐order equation reduces to Budden’s equation giving the well‐known transmission coefficient for both two‐ion hybrid and second‐harmonic resonance. The equation includes the effect of simultaneous minority fundamental and majority second‐harmonic cyclotron damping. The solutions of the second‐order equation as a function of n∥ give absorption transmission and reflection coefficients that agree well with the results based on models giving higher‐order differential equations and solved by means of much more complex numerical codes.