We describe the results of experiments designed to test for microwave enhancement of vacancy transport processes in NaCl. Experimental results indicate that intrinsic vacancy mobility is not enhanced by microwave fields. Instead, the evidence strongly suggests an enhancement of the driving force for charge transport. The experimental results display features consistent with a recent theory for microwave-enhanced driving forces in ionic conductors. PACS numbers: 66.30.Hs, 68.35.Fx A growing body of experimental data suggests that microwave heating of ceramic materials leads to enhanced diffusion or solid-state reaction rates when compared with conventional heating at the same temperature [1][2][3][4][5][6][7]. If microwave heating is perceived as a purely thermal process (by rapid equilibration of microwave energy to thermal energy of the material), then it is difficult to explain how microwave and conventional furnace heating can result in markedly different reaction rates. The several explanations attempted for these experimental observations fall into one of two classes: (1) nonequilibrium thermodynamics, and (2) "nonthermal" phenomena.First, it has been argued that most temperature diagnostics only measure surface temperature and are therefore unreliable indicators of internal bulk temperatures. With microwave heating of low-loss materials, inverted temperature profiles (interior hotter than surface) occur at steady state as heat is lost from the surface, and it has been proposed that the internal temperatures responsible for the solid-state reactions exceed the measured surface temperatures by tens to hundreds of degrees Celsius. However, in some of the experiments referenced above (such as Ref.[3]), the sample dimensions and microwave absorption rates are both very small and therefore inconsistent with temperature differences of 50 -200'C between the surface and interior.Several nonthermal hypotheses are based on the idea that microwave field disturbances of sufficient magnitude might enhance high-energy, nonthermal "tails" on ion energy or lattice phonon distributions [8,9]. Such effects would appear as an enhancement of ionic mobility or a lessening of the activation energy for ionic motion in such a lattice. However, calculations based on the phonon kinetic (Boltzmann) equation [10] indicate that these phenomena will be negligible for the microwave field intensities present in Refs. [1 -7]. Most recently, Rybakov and Semenov [11] have proposed a model in which the microwave field induces nearsurface oscillatory fluxes of ionic point defects that are rectified, yielding a net "ponderomotive" (time-averaged nonzero) transport of charged defects. In effect, the microwave field induces a nonequilibrium concentration of vacancies in a small region near the surface of the ionic crystal. Mass flow is required to reach this nonequilibrium condition, and because the vacancies are charged, there is also an induced charge How. If these nonlinear forces are large enough, they could explain the observations of micr...

Particle simulations compare the behavior of nonrelativistic sheet electron beams in uniform static and nonuniform time-harmonic magnetic fields. The time-harmonic fields are equivalent to periodically cusped magnetic (PCM) fields. While the sheet beam in a uniform field exhibits diocotron instability, the PCM-focused beam is stabilized by ponderomotive forces, in agreement with recent analytic predictions [J. Appl. Phys. 73, 4140 (1993)]. Mismatched PCM-focused beams exhibit envelope oscillation and initially rapid emittance growth followed by a region of slower increase, in agreement with a recent semianalytic Fokker-Planck model. PACS numbers: 41.85.Lc, 41.85.Ja, 52.30.Bt Sheet or ribbon electron beams are intrinsically well suited for use where high beam currents and small beam-channel clearances are required. Applications include high-average-power free electron lasers [1], conventional low-voltage microwave tubes [2], and quasioptical gyrotrons [3]. Other applications may include gas laser excitation and high-current electron accelerators. The principal advantage of sheet beams over round crosssection beams is that by spreading the current out in the wide transverse dimension, one can propagate high currents through small beam-channel clearances without excessive space charge repulsion. The principal disadvantage of sheet beams is their susceptibility to disruption and filamentation in uniform solenoidal focusing magnetic fields. This behavior arises from ExB drift velocity shear and is most commonly referred to as "diocotron" instability.Ponderomotive stabilization of instabilities is a familiar concept in plasma physics [4-6] and using ponderomotive forces to confine round cross-section electron beams is a familiar concept in accelerator physics [7,8]. As demonstrated in this Letter, periodically cusped magnetic (PCM) fields [2] provide both effective focusing and stabilization of the diocotron instability in nonrelativistic sheet electron beams.The ponderomotive force of interest to this work is illustrated by a time-harmonic magnetic field of the form B(y,t) -B 0^j -sin(co B t)y + B 0 cos(co B t)z .(1)These fields are applied to a sheet electron beam having a uniform charge density no, a thickness S in the y dimension, infinite width in the x dimension, and uniform velocity UQ along the z dimension. The equations of motion in the transverse Cx,j>) plane are x =-y~-E x + (D cz (t)y -Q) cy (t)uo, m y = -^-E y -co cz (t)x , (2b) m where co cy (t)=qB y (t)/m, CQ cz (t) = qB z (t)/m, and we as-sume that perturbations to the velocity along z are negligible, i.e., Z~UQ. We proceed to solve Eq.(2) using a multiple-time-scale approach, assuming that we can separate fluctuating quantities into linear sums of fast and slow time scale responses, e.g, JC(/) =Xf(t)+x s (t), y(t) -y/iri+ysit),etc. The magnetic field terms (oscillating with frequency Q>B) are assumed to be varying rapidly, while the electric field terms associated with beam space charge fluctuations are considered to be slowly varying. Assuming that...

A recent design concept for millimeter-wave free-electron lasers [J. Appl, Phys, 60, 521 (1986) Jwould require the stable propagation of a sheet electron beam through a narrow waveguide channel. Experimental results reported in this article support the feasibility of such a configuration by demonstrating the stable propagation of relativistic sheet electron beams through a narrow waveguide gap (3.2 mm) using focusing by a short-period electromagnet wiggler. 90% of the electron current in a loo-keV sheet electron beam was transmitted through a S-cm-Iong channel with peak wiggler fields of 800 G. Almost 80% of a 400-keV beam was similarly confined with a 16oo-G wiggler field. The data were consistent with single electron trajectory models, indicating that space-charge effects were minimal. No evidence of beam breakup or filamentation instabilities was observed.

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