Date 58 June 1995
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1995 International Conference on Plasma Science [papers in summary form only: conference record abstracts]

A perspective on RF vacuum electronics: innovations and recent advances
Summary form only given. Vacuum electronics continues as a vital technology for the generation of coherent radiation in a spectral region extending from the UHF to the infrared. Many of the advances and innovations from current R&D efforts are associated with two primary technological thrusts. First is the continuing development of fastwave device concepts for use in heating, particle acceleration, and RF power transmission. While efficient, highpower oscillators are sufficient for heating, coherent sources are preferred for particle acceleration and radar. For these applications, the performance requirements are more strenuous, including such features as instantaneous bandwidth, stability, linearity, and noise as well as packaging. Exemplifying this thrust is the development of a secondgeneration of fastwave amplifiers based on the electron cyclotron resonance and the free electron masers and the gyropeniotron. The second thrust is defined by the creative blending of solidstate and vacuum concepts, techniques and capabilities. The microwave power module, a new transmitter archetype, highlights the benefits of this approach. More speculatively, RF vacuum microelectronics combines the advantages of electron transport in vacuum with gated emission structures derived from solidstate microfabrication. The advent of practical gated vacuum emitters, based on this approach, is expected to have a strong impact on RF source technology. These recent advances and new opportunities are indicative of a growth potential that confirms RF vacuum electronics as a technology fully capable of meeting the challenges of the future. View full abstract»

Energy transport benchmark for nonhomogeneous target plasmas
Summary form only given, as follows. Plasma stream target interactions at the MW/cm/sup 2/ power density level of the impacting source result in immediate evaporation of target material and in early formation of a protective plasma shield in front of the target. The target plasma for low Z materials is a two zone plasma with a hot low dense plasma corona and a cold rather dense plasma layer towards the target. The plasma corona in which the plasma stream is stopped converts the incoming energy with an efficiency of up to 50 % into soft Xray (SXR) radiation. The energy transport in such a plasma shield has to deal with the transfer of intense SXR radiation through cold and dense plasma layers and has to take into account reabsorption of the SXR line radiation in the cold plasma. To describe such processes a selfconsistent approach in which the interaction of the radiation field with the plasma locally is taken into account is required. A comparison of results from opacity and selfconsistent approach clearly demonstrates an increase in energy transfer through the plasma shield in case of the selfconsistent approach of a factor of 4 for a power density of the impinging beam of 10 MW/cm/sup 2/. To check the adequacy of the selfconsistent approach energy transfer benchmark calculations were performed at CEA, FZK, LLNL and Lykov for nonhomogeneous beryllium and carbon plasma shields. The paper describes the benchmark and the models used in the different calculations and gives a discussion of the different results obtained. View full abstract»

Threedimensional RayleighTaylor instability in Saturn zpinch implosions: a study with MACH3
Summary form only given. A new portable parallel physics simulation code, called MACH3 (multiblock arbitrary coordinate hydrodynamics code in three spatial dimensions), has been developed by the Phillips Laboratory for performing three dimensional collisional plasma simulations. This code is based on the widelyused and useful twodimensional code, MACH2. Both are arbitrary Lagrangian Eulerian codes with sophisticated physics and numerical models to allow the user great flexibility in solving nonideal magnetohydrodynamic (MHD) problems. A preliminary series of calculations has been performed to investigate threedimensional effects in an imploding annular plasma gas puff driven by the Saturn pulsed power generator at Sandia. Plasma instabilities are seeded by an initial periodic density perturbation in the azimuthal direction, with a random component in the rz plane. Results show the interaction between the rz plane and the r/spl thetav/ plane modes and their effect on the sheath dynamics during the /spl sim/65 ns implosion. Comparison between calculations using MACH2 and MACH3 show the degree of applicability of the premise of the dominance of rz plane growth usually made to justify 2dimensional simulations. View full abstract»

Assessment of computational methods for simulating AC plasma display panels
Page(s): 93  94Summary form only given. This paper compares fluid and particle simulations for configurations typical of doublesubstrate AC plasma display panels. The purpose is to test the validity of various approximations used in fluid simulation codes. For fluid simulations, assumptions are usually made regarding the dependence of the electron transport and rate coefficients on, for example, the local and instantaneous value of the electric field. The use of the local field approximation is tested by comparing with a fullykinetic code based on a particleincell/MonteCarlo collision simulation. We observe that the local field approximation fails to describe the electron and ion kinetics in the presence of large field nonuniformities in the cathode fall region. This leads to large discrepancies in the voltage transfer curve and the sustaining voltage margin. The comparison to the particle simulations is significantly improved by adding the energy and momentum relaxation equations in the fluid description of the electron and ion kinetics, respectively. The level of sophistication used to describe the dynamics of the discharge in plasma display panels will determine how computationally intensive and how practical the model is. View full abstract»

Neutral species densities in an electron cyclotron resonance CF/sub 4/ plasma etching system
Summary form only given. A new procedure for the calculation of neutral transport at long meanfree paths is applied to describing plasma chemistry in a low neutral pressure high plasma density plasma etching reactor. The Electron Cyclotron Resonance (ECR) etching system is run with CF/sub 4/ feed gas at pressures from less than one mTorr to around ten mTorr. In this pressure regime, the meanfreepath of neutral molecules if on the order of the diameter of the system, limiting the application of fluid models. A novel propagator method has been developed which is well suited to the longmeanfree path regime for multiple, interacting and reacting neutral species. The calculation of the propagators allows for various effects such as variable meanfreepath and anisotropic scattering. The effects of truncating the hot tail of the electron distribution function are shown to be relatively small provided the power deposition by electrons into the neutral gas is held constant. View full abstract»

Modelling of RF glow discharges by direct numerical procedure of the Boltzmann equation
Page(s): 94  95Summary form only given. In our previous papers, we performed a direct numerical procedure (DNP) of the Boltzmann equation with an algorithm without any expansion of the velocity distribution in spatial homogeneity, in order to study radio frequency (RF) electron transport. We further developed and applied the DNP to the modeling of an RF glow discharge with space and time variation of the electron velocity distribution. It has a great advantage in that the nonequilibrium characteristics of transport electrons can be exactly expressed without statistical error. Only collision cross section of the electron with the molecular are required for calculation without swarm parameters as for electrons, when the governing equation system is numerically simulated. The boundary condition more appropriate both for the electrode surfaces will be introduced, since the velocity (energy) distribution function of electrons between electrodes and on the surface are direct obtained from the series of calculations. Capacitively coupled parallel plate discharge with 20 mm spacing is considered in the present modeling in order to simplify the model and to compare the plasma structure with our previous result using relaxation continuum model. Non reactive Ar with simple cross sections is employed as the source gas. View full abstract»

A comparison of three velocity discretizations for the Vlasov equation
Summary form only given. Three different methods of velocity discretization for the Vlasov equation are compared for use in the numerical solution of the onedimensional Vlasov equation. The first method is a simple central difference on a uniform grid in velocity space; with this method the evaluation of the right hand side of the Vlasov equation requires 8 floating point operations per degree of freedom. The other two methods are weighted residuals methods based on Hermite polynominals: the first of these is based on expansion functions and identical weight functions; the second Hermite based method uses expansion functions and different weight function. These two methods require 12 and 8 floating point operations per degree of freedom respectively. Thus all three methods require the same order of computational work, however, for finite numbers of degrees of freedom the finite difference method conserves only particles, the symmetric Hermite method conserves either particles or momentum, while the asymmetric Hermite method conserves particles, momentum, and energy. The two Hermite methods also exactly recover the Hermite moments of the free streaming solution of the Vlasov equation, and the asymmetric Hermite method exactly solves the spatially uniform VlasovAmpere equations (exact plasma oscillations). When used to compute the growth rates of unstable plasma equilibria the finite difference method shows only algebraic convergence, while both Hermite based methods show spectral convergence, with the error decay rate for the asymmetric Hermite method larger than for the symmetric Hermite. View full abstract»

Two dimensional PIC simulation of a Langmuir probe in a plasma beam
Summary form only given, as follows. A 2d/3v electrostatic particleincell (PIC) code has been developed to simulate a Langmuir probe in a plasma beam. The code was written to enable the use of the Langmuir probe in plasma regimes for which no closedform analytical solutions exist; this is the case for a probe in an ion beam, such as the plume of an ion thruster. Langmuir probes are used to determine local plasma properties, such as electron temperature, by careful dissection of the probe's VI characteristic. To interpret experimental data from a Langmuir probe, one must separate ion from electron current. This process is well documented for quiescent plasmas; however, no systematic techniques are available for interpreting data obtained using an electric probe in an ion beam ad hoc estimates of probe ion current in beam plasmas may lead to order of magnitude errors in the calculation of electron temperature. The PIC code described in this paper was written to elucidate the beamprobe interaction and provide systematic techniques for legitimately interpreting experimental data. Elements of the PIC technique in general will be discussed; in particular, methods used in fluxing particles across boundaries. Code results will be presented. Code and theoretical probe traces for an infinite cylindrical probe in a quiescent plasma will be shown to be in agreement. Also, code results for a plasma beam will be compared with experimental data from the UTSI threegrid ion thruster. View full abstract»

Threedimensional simulation of helix travelling wave tubes
Summary form only given. We present a threedimensional nonlinear formulation and simulation of a helix travelling wave tube (TWT) using a sheath helix model. The simulation is capable of treating both DC and pulsed electron beams as well as singlefrequency or multitone operation. The model relies upon a spectral decomposition of the electromagnetic fields in terms of the vacuum sheath helix polarizations. A Poyntinglike equation describes the energy balance. The electron orbits are treated using the complete Lorentz force equations. The field equations are integrated on a grid and advanced in time using a MacCormack predictorcorrector scheme, and the electron orbit equations are integrated using a fourth order RungeKutta algorithm. Charge is accumulated on the grid and the field is interpolated to the particle location by a linear map. Several numerical cases are considered. Simulation of the injection, of a DC beam and a signal at a single frequency is compared with a linear field theory of the helix TWT interaction, and good agreement is found. Simulation of a prebunched beam is also discussed. View full abstract»

Cyclotron effects in relativistic backward wave oscillators
Summary form only given, as follows. The operation of high power Cherenkov devices such as backward wave oscillators is based on the interaction of high current, relativistic electron beams with synchronous electromagnetic fields of periodically corrugated waveguides. The high current electron beam is guided by a strong axial magnetic field. Therefore, in addition to the Cherenkov synchronism, the cyclotron resonance conditions can be realized for different spatial harmonics of both forward and backward waves. The cyclotron interaction manifests itself in the output power dependence on the axial focusing magnetic field. We developed linear and nonlinear theories that predict this dependence and the results from the numerical modeling compared favourably with the existing experimental data. We also found that the combined Cherenkov and cyclotron interaction may result in a higher efficiency conversion of the electron beam energy into radiation. View full abstract»

Advances in the understanding of efficient operation of high power backwardwave oscillators
Page(s): 96  97Summary form only given. Recent work has shown that the efficiency of converting electron beam energy to microwave energy in a backward wave oscillator (BWO) depends very strongly on reflections within the slow wave structure (SWS), and on the interaction of the electron beam with the forward travelling harmonics. The latter result differs from earlier work where it was indicated that the electron beam cannot interact with forward travelling harmonics. Experiments were performed at UNM using the Sinus6 relativistic electron beam accelerator and an Xband BWO comprised of uniform amplitude corrugations. Sections of smoothwalled waveguide having different lengths were inserted between the BWO and the upstream cutoff neck. Results from these experiments show that the radiated power and oscillation frequency are periodic functions of the length of the smoothwalled waveguide. Particleincell simulations of the experiments predict similar behaviour. Simulations show that the transverse magnetic wave is dominated by fast, backward and forward travelling space harmonics, and the slow, backward travelling harmonic associated with the corrugated structure. The periodic variation of output power and oscillation frequency with the length of the smoothwalled waveguide is well correlated with the constructive and destructive interference of the dominant space harmonics, which form a standing wave in the region between the cutoff neck and SWS. View full abstract»

Experiments on folded waveguide gyroTWT amplifier
Summary form only given, as follows. Experiments on a folded waveguide gyroTWT amplifier are underway to demonstrate high power (>50 kW), broadband (BW>15%), Kaband radiation amplification. The interaction circuit is a periodic, Hplane bend, transverse folded waveguide employed with a high power axisencircling electron beam. The electron beam with a large transverse momentum is produced by an advanced triplepolepiece centerpost electron gun designed by Litton for NRL millimeter wave gyroamplifier experiments. For a proofofprinciple experiment, a low gain 12 period circuit is built and tested. A mode coalescing of the first stopband predicted by an equivalent circuit model and a 3D electromagnetic code is verified from experimental measurements. Measurements show a return loss of <15 dB over the frequency bandwidth of >20%. Experimental data are presented and compared with slowtime scale nonlinear code simulations. View full abstract»

Nonlinear theory of slow cyclotron wave interaction in folded waveguide
Summary form only given, as follows. A threedimensional nonlinear theory is presented for the generation of broadband radiation from slow cyclotron wave interaction in a folded waveguide. The serpentine structure is formed by folding a rectangular waveguide so that the orientation of the magnetic changes (Hplane bend) instead or the conventional Eplane bend configuration where the orientation of the electric field changes. The Hplane bend structure can use larger beam tunnel without distorting the RF field structure and generate higher output power. Numerical results are shown for the TE/sub 10/ mode propagation in an unridged and a double ridged waveguide. For a 61.5 kV, 3 A beam with /spl alpha/=1.0 and /spl Delta/V/sub Z//V/sub Z/=0, calculations show an efficiency of 25% with 20% bandwidth and an efficiency of 35% at 10% bandwidth. The efficiency and bandwidth is relatively unchanged up to a beam axial velocity spread of 2%. The bandwidth can be further increased by mode coalescing techniques. Multistage operation is necessary to avoid backward wave oscillation. View full abstract»

Experimental studies and sheet beam transport for lowvoltage, grating TWT amplifiers
Summary form only given, as follows. Spontaneous emission and linear gain measurements for a lowvoltage sheetbeamcompatible, grating TWT amplifier are presented. Results of analyses of a sheet beam formation by magnetic quadrupoles from a round beam and staple transport in a periodic cusp magnetic field are also discussed. A round "probe" beam from a 10 kV, 0.25 A Pierce gun electron source is utilized for 14 GHz amplifier experiments. The spontaneous emission measurements provide (a) measurement of the gratinginduced spontaneous emission spectrum which can be correlated with the theoretically predicted linear gain curves, (b) measurements of broadband noise emission, and (c) measurement of spontaneous emission in the backwardwave regime to correlate with start oscillation predictions. The noise emission spectra have been correlated with experimental factors including the guide magnetic field intensity and body current. Measurements of linear gain are also compared with the theoretical prediction in both forward and backwardwave regimes. A sheet beam can be formed by the use of magnetic quadrupoles to transform an initially round beam from a conventional Pierce gun into a highly eccentric elliptical beam. Results of a 3D PIC simulation of the beam will be discussed. View full abstract»

Insitu experimental investigations of electron spacecharge instabilities and noise mechanisms in a reentrant crossedfield amplifier via distributedcathode emission and gatedbeam injection
Summary form only given. Experimental investigations of the true physical conditions inside the crossedfield devices are of fundamental importance for the understanding of the operation of these devices and may lead to eventual improvement of the present tubes. At Northeastern University, tube research has taken up a combined approach of in situ plasma diagnostics and computer simulations using two frequency scaled CFAs as test vehicles. A collection of temporal and timeaveraged diagnostic techniques have been developed through our research. Probe measurements as well as device performance of the linear CFA and the beaminjected, reentrant CFA have been directly compared with computer simulation results from MASK and NEAMP codes. We have recently incorporated in our reentrant CFA a secondary emission cathode for the purpose of gaining insight on improving the noise performance of both military and commercial devices. It has long been speculated and appears more so as a result of the improved diagnostic techniques, that the instabilities in the space charge cloud are the major source of noise in crossedfield devices. The average electron transit time is determined experimentally through a gatedelectron injection scheme. Latest results are reported. View full abstract»

Measurement, modelling, and simulation of drift space leakage signals in crossedfield amplifiers
Summary form only given, as follows. Previous experimental results have indicated an RF signal leakage through the drift space of CrossedField Amplifiers (CFAs). We have collected frequency swept Sparameter data for both CFA on and off conditions and transformed these results to the time domain. Two time signals in addition to the main path signal have been found in S/sub 21/(t) data, which originate from drift space leakage. One of the additional time signals precedes the main path signal and the other is delayed with respect to the main path signal. The preceding time signal is due to a quick passage path from input to output, without ever entering the main path slowwave circuit. The delayed time signal originates from a signal which travels along the slowwave circuit, passes through the drift space, and travels along the slowwave circuit a second time before exiting the CFA as output. We have confirmed the presence of three time signals in CFA off response by conducting realtime digitization experiments. A model has been developed to describe leakage and main path signals, as well as a method of determining model parameters from Sparameter values. The inclusion of RF drift space leakage in the MASK simulation program is achieved by introducing a feedback impedance, with an impedance value determined using measured Sparameter results and MASK slowwave circuit model parameters. The importance of RF drift space leakage on amplifier performance characteristics such as signal to noise ratio are emphasized. View full abstract»

Internal feedback and its effect on phase linearity in a forward wave crossedfield amplifier
Summary form only given, as follows. Two sources of internal feedback couple the input and output of crossedfield amplifiers (CFAs). Direct RF feedback occurs because the ends of the slow wave circuit radiate energy into the drift space connecting the output and input; the magnitude of this type of feedback may be measured at cold test. Electronic feedback, on the other hand, occurs only when the tube is operating, and is much harder to measure. It is due to the residual coherency retained by the beam after its passage through the drift space. In the forward wave case, this feedback can still induce significant currents at the beginning of the slow wave circuit that must be added vectorially, along with the direct RF feedback signal, to the input signal to produce an effective drive signal. This effective drive signal is therefore shifted in both amplitude and phase from the input signal, though the phase shift is generally more important than the amplitude shift in saturated amplifiers. The reentrant current also contains certain random components that add to the input signal and contribute to CFA noise. As the input signal frequency of the amplifier is varied, the difference in electrical path length around the tube leads to a periodic variation of the total feedback signal relative to that of the input signal, resulting in a variation in phase of the effective drive signal, which in turn produces a periodic variation in phase of the output signal. This variation can have significant consequences for the system in which the CFA is used. The magnitude of this variation is very difficult to estimate other than by the use of a simulation code. We have applied our CFA simulation code, MASK, to this problem and have produced very good agreement with measurements of output phase versus frequency for a high power, forward wave Sband tube. View full abstract»

Analytic formulas for magnetron characteristic curves
Page(s): 99  100Summary form only only given, as follows. A closed nonlinear set of equations is obtained based on the guiding center fluid model to describe steadystate magnetron operation. Spoke charge effects are included selfconsistently, by introducing a meanfield approximation so that the effective AC potential preserves the geometric similarity with the vacuum solutions. The characteristic equations, relating the anode current I and the RF power P to the applied DC voltage V at given RF frequency, are obtained. The dynamic impedance R, the electronic efficiency /spl eta/ and the constant /spl beta/ are computed at synchronism V=V/sub s/, where V/sub s/ is the BunemanHartree voltage. Operation in that range is characterized by the maximum achievable spoke current (saturation) at given AC voltage. Outside that range the departure from synchronism limits the current that reaches the anode. The two current cutoff voltages well above and below V/sub s/ are also obtained. Previously obtained VI equations disagree with experiments in that (a) anode current and RF power go to zero when the resonance condition V=V/sub s/, is met, (b) the operation voltage V is a doublevalued function of the current I; there exist two nearly symmetric operation points around V/sub s/ at the same current I. Yet magnetrons, and the related crossedfield amplifiers, are known to exhibit stable operation with single valued VI characteristics well below V/sub s/. Although zero gain at Synchronism applies to other microwave devices (TWTs, FELs), experimental results and particle simulations of crossed field devices suggest otherwise. View full abstract»

Photon interaction with beamplasma induced electromagnetic turbulence
Summary form only given, as follows. Photon interaction with plasma turbulence induced by relativistic beamplasma instability is studied by 2 and 1/2 D particle simulation code MAGIC. A relativistic beam with a typical Lorentz factor of /spl gamma/=10 to 40 and a beam density of n/sub b/=0.02n/sub o/ is used to induce the beamplasma instability in a collisionless plasma (n/sub o/=1/spl times/10/sup 18/ m/sup 3/, T/sub c/=10 keV). The relativistic beam induces the instability through coupling between the beamplasma mode and an electromagnetic mode resulting in electromagnetic turbulence. The observed growth rate of the instability, as a function of beam velocity and wavevector, agrees well with linear theory. Photonplasmon interaction is studied by injecting a photon, with frequency on the order of /spl omega//sub pe/, into the plasma turbulence. The interaction between the injected photon and the plasma turbulence is analyzed in the frequency domain as well as wavevector domain. The beamplasma induced turbulence generates wavevector modes which can couple into the photon field. Energy from the plasma turbulence has been transferred to the photon increasing the photon frequency to 2/spl omega//sub pe/. The energy absorbed is a fraction of the incoming photon energy. The interaction is found to depend on the beamplasma instability, disappearing when the beamplasma instability is suppressed. View full abstract»

Dust particles charging in nonMaxwellian plasmas
Summary form only given, as follows. Dust contaminants play an important role in many industrial applications of plasma sciences and in space plasmas. The behaviour of dust particles immersed in plasmas is well understood in many physical situations. The charging of a dust particle under the bombardment of electrons and ions from a Maxwellian plasma has been studied in many papers. The net charge deposited on a dust particle can show fluctuations in time, but a steady state is reached. Theoretical, numerical and experimental work has shown the main features of the interactions between dust particles and Maxwellian plasmas. Recently, a number of papers have investigated with particleincell (PIC) methods the details of the process of dust charging. The theoretical results have been confirmed. However, the studies, theoretical or numerical, have been limited to Maxwellian plasmas. In many physical situations this assumption is not acceptable. As an example, in many plasmaprocessing devices the dust particles have been shown to collect at the edge of the cathode sheath, where the ion and electron velocity distributions clearly have deviations from a Maxwellian equilibrium. In the present work we have investigated the effect of nonMaxwellian distributions and drift velocities, using simulation methods based on the PIC approach. View full abstract»

High frequency bursts at a double layer
Summary form only given. The high frequency (hf) oscillations which are driven by the electron beam on the high potential side of an electric double layer are investigated in a laboratory experiment where the current is drawn out from a magnetic mirror. Two innovations in hf probe design have made it possible to achieve a combination of absolute amplitude calibration and spatial resolution which, for such high frequencies, have never been achieved before. The influence of the hf region on the surrounding plasma is important, for example, for the matching of space double layers to the surroundings. We have therefore investigated how the hf region influences the double layer discharge physics, focusing on the energy and particle balance. Up to 20% of the beam energy is converted to oscillations within a region which extends from 100 to 400 Debye lengths from the double layer, on the high potential side. This makes, with our discharge parameters, the hf waves more efficient than inelastic collisions to locally deposit beam energy in the anode plasma. On stationary probes, amplitude variations are found which closely resemble bursty plasma waves observed in space. The interpretation of such data is difficult in space where it might be difficult even to distinguish between spatial and temporal variations. Our experiment can be regarded as a detailed case study of one example of such bursts. View full abstract»

Confinement in time dependent traps
Page(s): 101  102Summary form only given, as follows. Time dependent confining fields have been widely used for high precision spectroscopy measurements during the last decades. In addition, there has been a renewed interest in the field of particle confinement in trapping fields for low power fusion devices, dusty plasmas and advanced chemical processing. We study the confinement of charged particles by time dependent, linear and nonlinear, fields with arbitrary pulse shape. We assumed that the trapped particles are perturbed by collisions with a background gas or any other source of momentum fluctuations. The basic parameters of the confinement are determined using asymptotic expansions based on singular perturbation techniques. Parametric instabilities, which result in the loss of confinement, are identified for different field strengths and pulse shapes. View full abstract»

Dynamic and Debye shielding and antishielding in magnetized, collisionless plasmas
Summary form only given, as follows. Collisionless shielding in one dimensional (highly magnetized) plasmas is paradoxical. The insertion of a positive test charge into such a plasma locally accelerates the plasma electrons causing them to move faster in the vicinity of the test charge. Since flux conservation requires that faster moving electrons have lower density, the density of the negatively charged electrons will decrease around the test charge. The plasma antishields the test charge; instead of decreasing the net positive charge near the test particle, the plasma will increase the net charge. This phenomena has been sporadically recognized in the literature, but, to our knowledge, has never before been observed. While we observe antishielding in a pure electron plasma when we employ unusual initial conditions, more commonly we observe the converseshielding. We show that this shielding results from the presence of electrons trapped in the potential well of the test charge. While several different mechanisms are observed to trap electrons, an ubiquitous, fast acting, transittime mechanism always traps electrons when the test charge is introduced adiabatically. That one dimensional (1d), collisionless shielding requires trapping does not appear to have been previously recognized and the explanation of shielding given in many textbooks and papers is incorrect or incomplete. Because the trapping results from dynamical processes, we call the resulting shielding "dynamic" shielding. Both the observed and calculated magnitude of dynamic shielding can be significantly smaller than Debye shielding; eventually collisions transform the dynamic shielding to Debye shielding. View full abstract»

Adiabatic change of state of photon gas
Summary form only given as follows. We previously introduced and justified the k problem as a thermodynamical contradiction of photon gas. In the thermodynamics of a photon gas the main contradiction is called the k problem; the piezotropic autobarotropic equation of state P=u/3 is adiabatic if k=1 exclusively, while the adiabatic connection PV/sup 4/3/=const (or rather the Poisson equation P/sub /spl thetav///sup 4/3/=const, /spl thetav/=u/c/sup 2/) requires that k=4/3. The present paper shows that the equations of state PV/sup 4/3/=const, TV/sup 1/3/=const, T/sup 4/3/P/sup 1/3/=const and P=u/3 cannot be valid for the adiabatic change of state of photon gas, simultaneously. Furthermore, Planck's distributionand so the Wien's law and the RayleighJeans connection as wellcannot be invariant in case of adiabatic change of state of photon gas. Namely, in case of adiabatic change of state of photon gas, a new type of ultraviolet catastrophe appears. These results are of fundamental importance in the case of arbitrary deformation of electromagnetic radiation fields or quantum plasmas. View full abstract»