Volume 23, Issue 9, September 2016

TrivelpieceGould (TG) modes originally described electrostatic surface waves on an axially magnetized cylindrical plasma column. Subsequent studies of electromagnetic waves in such plasma columns revealed two modes, a predominantly magnetic helicon mode (H) and the mixed magnetic and electrostatic TrivelpieceGould modes (TG). The latter are similar to whistler modes near the oblique cyclotron resonance in unbounded plasmas. The wave propagation in cylindrical geometry is assumed to be paraxial while the modes exhibit radial standing waves. The present work shows that TG modes also arise in a uniform plasma without radial standing waves. It is shown experimentally that oblique cyclotron resonance arises in large mode number helicons. Their azimuthal wave number far exceeds the axial wave number which creates whistlers near the oblique cyclotron resonance. Cyclotron damping absorbs the TG mode and can energize electrons in the center of a plasma column rather than the edge of conventional TG modes. The angular orbital field momentum can produce new perpendicular waveparticle interactions.
 LETTERS


Kinetic equation for nonlinear resonant waveparticle interaction
View Description Hide DescriptionWe investigate the nonlinear resonant waveparticle interactions including the effects of particle (phase) trapping, detrapping, and scattering by highamplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of waveparticle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a FokkerPlanck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phasespace via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.

Effects of energetic particles on zonal flow generation by toroidal Alfvén eigenmode
View Description Hide DescriptionGeneration of zonal flow (ZF) by energetic particle (EP) driven toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual mesoscale and microscale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.

What is the surface temperature of a solid irradiated by a Petawatt laser?
View Description Hide DescriptionWhen a solid target is irradiated by a Petawatt laser pulse, its surface is heated to tens of millions of degrees within a few femtoseconds, facilitating a diffusive heat wave and the acceleration of electrons to MeV energies into the target. Using numerically converged collisional particleincell simulations, we observe a competition between two surface heating mechanisms–inverse bremsstrahlung in solid density on the one hand and electron scattering on turbulent electric fields on the other. Collisionless heating effectively dominates above the relativistic intensity threshold. Our numerical results show that a highcontrast 40 fs, f/5 laser pulse with 1 J energy will heat the skin layer to 5 keV, and the inside of the target over several microns deep to bulk temperatures in the range of 10–100 eV at solid density.

Charged particle dynamics in the presence of nonGaussian Lévy electrostatic fluctuations
View Description Hide DescriptionFull orbit dynamics of charged particles in a 3dimensional helical magnetic field in the presence of αstable Lévy electrostatic fluctuations and linear friction modeling collisional Coulomb drag is studied via Monte Carlo numerical simulations. The Lévy fluctuations are introduced to model the effect of nonlocal transport due to fractional diffusion in velocity space resulting from intermittent electrostatic turbulence. The probability distribution functions of energy, particle displacements, and Larmor radii are computed and showed to exhibit a transition from exponential decay, in the case of Gaussian fluctuations, to power law decay in the case of Lévy fluctuations. The absolute value of the power law decay exponents is linearly proportional to the Lévy index α. The observed anomalous nonGaussian statistics of the particles' Larmor radii (resulting from outlier transport events) indicate that, when electrostatic turbulent fluctuations exhibit nonGaussian Lévy statistics, gyroaveraging and guiding centre approximations might face limitations and full particle orbit effects should be taken into account.

Parametric sum envelope instability of periodically focused intense beams
View Description Hide DescriptionThe envelope instability is a second order parametric resonance with the periodic focusing and known to appear in space charge dominated beams near 90° phase advance per focusing period. We show in 2d approximation that space charge may also induce parametric “sum envelope instabilities” leading to simultaneous growth of envelopes or skew angles as well as emittances. This can happen by twoplane envelope coupling or by exciting a skew (“odd”) mode in an otherwise fully uncoupled linear lattice. At resonance, the two individual phase advances are split more or less symmetrically away from 90°, and exponential growth occurs. Results from perturbation theory are compared with full envelope models, particleincell simulations, and smooth approximation stopband calculations, all showing very good agreement for realistic space charge parameters.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Stability of Brillouin flow in the presence of slowwave structure
View Description Hide DescriptionIncluding a slowwave structure (SWS) on the anode in the conventional, planar, and inverted magnetron, we systematically study the linear stability of Brillouin flow, which is the prevalent flow in crossedfield devices. The analytic treatment is fully relativistic and fully electromagnetic, and it incorporates the equilibrium density profile, flow profile, and electric field and magnetic field profiles in the linear stability analysis. Using parameters similar to the University of Michigan's recirculating planar magnetron, the numerical data show that the resonant interaction of the vacuum circuit mode and the corresponding smoothbore diocotronlike mode is the dominant cause for instability. This resonant interaction is far more important than the intrinsic negative (positive) mass property of electrons in the inverted (conventional) magnetron geometry. It is absent in either the smoothbore magnetron or under the electrostatic assumption, one or both of which was almost always adopted in prior analytical formulation. This resonant interaction severely restricts the wavenumber for instability to the narrow range in which the cold tube frequency of the SWS is within a few percent of the corresponding smooth bore diocotronlike mode in the Brillouin flow.

The charge imbalance in ultracold plasmas
View Description Hide DescriptionUltracold plasmas are regarded as quasineutral but not strictly neutral. The results of charge imbalance in the expansion of ultracold plasmas are reported. The calculations are performed by a full moleculardynamics simulation. The details of the electron velocity distributions are calculated without the assumption of electron global thermal equilibrium and Boltzmann distribution. Spontaneous evolutions of the charge imbalance from the initial states with perfect neutrality are given in the simulations. The expansion of outer plasma slows down with the charge imbalance. The influences of plasma size and parameters on the charge imbalance are discussed. The radial profiles of electron temperature are given for the first time, and the selfsimilar expansion can still occur even if there is no global thermal equilibrium. The electron disorder induced heating is also found in the simulation.

TrivelpieceGould modes in a uniform unbounded plasma
View Description Hide DescriptionTrivelpieceGould (TG) modes originally described electrostatic surface waves on an axially magnetized cylindrical plasma column. Subsequent studies of electromagnetic waves in such plasma columns revealed two modes, a predominantly magnetic helicon mode (H) and the mixed magnetic and electrostatic TrivelpieceGould modes (TG). The latter are similar to whistler modes near the oblique cyclotron resonance in unbounded plasmas. The wave propagation in cylindrical geometry is assumed to be paraxial while the modes exhibit radial standing waves. The present work shows that TG modes also arise in a uniform plasma without radial standing waves. It is shown experimentally that oblique cyclotron resonance arises in large mode number helicons. Their azimuthal wave number far exceeds the axial wave number which creates whistlers near the oblique cyclotron resonance. Cyclotron damping absorbs the TG mode and can energize electrons in the center of a plasma column rather than the edge of conventional TG modes. The angular orbital field momentum can produce new perpendicular waveparticle interactions.

Existence regimes for the formation of nonlinear dissipative structures in inhomogeneous magnetoplasmas with nonMaxwellian electrons
View Description Hide DescriptionNonlinear dissipative structures are studied in one and two dimensions in nonuniform magnetized plasmas with nonMaxwellian electrons. The dissipation is incorporated in the system through ionneutral collisions. Employing the drift approximation, nonlinear drift waves are derived in 1D, whereas coupled driftion acoustic waves are derived in 2D in the weak nonlinearity limit. It is found that the ratio of the diamagnetic drift velocity to the velocity of nonlinear structure determines the nature (compressive or rarefactive) of the shock structure. The upper and lower bounds for velocity of the nonlinear shock structures are also found. It is noticed that the existence regimes for the drift shock waves in one and two dimensions for Cairns distributed electrons are very distinct from those with kappa distributed electrons. Interestingly, it is found that both compressive and rarefactive shock structures could be obtained for the one dimensional drift waves with kappa distributed electrons.

Interaction of highpower microwave with air breakdown plasma at low pressure
View Description Hide DescriptionThe highpower microwave breakdown at the low air pressure (about 0.01 atm) is simulated numerically using the onedimensional model coupling Maxwell's equations with plasma fluid equations. The accuracy of the model is validated by comparing the breakdown prediction with the experimental data. We find that a diffuse plasma with a stationary front profile forms due to the large electron diffusion. Most of the incident wave energy is absorbed and reflected by the plasma when the plasma front achieves a stationary profile. The front propagation velocity remains almost unchanged with time and increases when the incident wave amplitude increases or the incident wave frequency decreases. With the incident wave frequency increasing, the maximum density of the stationary plasma front increases, while the ratio of the reflected wave power to the incident wave power remains almost unchanged. At a higher incident wave amplitude, the maximum density and reflectance become large.

Neutral and nonneutral collisionless plasma equilibria for twisted flux tubes: The GoldHoyle model in a background field
View Description Hide DescriptionWe calculate exact onedimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the “forcefree” GoldHoyle magnetic flux tube embedded in a uniform and antiparallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly forcefree, but by reducing its magnitude, the departure from forcefree can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely, the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's equation and Ampère's law are solved exactly, and the solution allows either electrically neutral or nonneutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space, and astrophysical contexts, as well as in the laboratory.

Generation of coherent ion acoustic solitary waves in inhomogeneous plasmas by an odd eigenmode of electron holes
View Description Hide DescriptionGeneration of coherent ion acoustic solitary waves (IASWs) in inhomogeneous plasmas by an odd eigenmode (OEM) of electron holes (EHs) is investigated using 1D electrostatic particleincell (PIC) simulations. The OEM oscillates at a frequency comparable to the trapped electron bouncing frequency, as also demonstrated by Lewis' theoretical formalism about the linear eigenmode in BernsteinGreeneKruskal (BGK) equilibrium. The density gradient in the inhomogeneous plasmas causes asymmetry in the EH potential structure associated with the OEM, whose amplitude grows rapidly as it propagates through the density gradient region. As the ions interact with this asymmetric potential, which oscillates slowly enough for the ions to respond, they are ejected to the lower density side with a larger potential amplitude, forming a chain of IASWs coherently with the oscillation of the OEM.

Hamiltonian particleincell methods for VlasovMaxwell equations
View Description Hide DescriptionIn this paper, we study the VlasovMaxwell equations based on the MorrisonMarsdenWeinstein bracket. We develop Hamiltonian particleincell methods for this system by employing finite element methods in space and splitting methods in time. In order to derive the semidiscrete system that possesses a discrete noncanonical Poisson structure, we present a criterion for choosing the appropriate finite element spaces. It is confirmed that some conforming elements, e.g., Nédélec's mixed elements, satisfy this requirement. When the Hamiltonian splitting method is used to discretize this semidiscrete system in time, the resulting algorithm is explicit and preserves the discrete Poisson structure. The structurepreserving nature of the algorithm ensures accuracy and fidelity of the numerical simulations over long time.

High order volumepreserving algorithms for relativistic charged particles in general electromagnetic fields
View Description Hide DescriptionWe construct high order symmetric volumepreserving methods for the relativistic dynamics of a charged particle by the splitting technique with processing. By expanding the phase space to include the time t, we give a more general construction of volumepreserving methods that can be applied to systems with timedependent electromagnetic fields. The newly derived methods provide numerical solutions with good accuracy and conservative properties over long time of simulation. Furthermore, because of the use of an accuracyenhancing processing technique, the explicit methods obtain highorder accuracy and are more efficient than the methods derived from standard compositions. The results are verified by the numerical experiments. Linear stability analysis of the methods shows that the high order processed method allows larger time step size in numerical integrations.

Nonlinear ion acoustic dissipative shock structure with exchangecorrelation effects in quantum semiconductor plasmas
View Description Hide DescriptionIon acoustic shocks in the electronholeion semiconductor plasmas have been studied. The quantum recoil effects, exchangecorrelation effects and degenerate pressure of electrons and holes are included. The ion species are considered classical and their dissipation is taken into account via the dynamic viscosity. The Korteweg de Vries Burgers equation is derived by using reductive perturbation approach. The excitation of shock waves in different semiconductor plasmas is pointed out. For numerical analyses, the plasma parameters of different semiconductors are considered. The impact of variation of the plasma parameters on the strength of the shock wave in the semiconductor plasmas is discussed.

Investigation of magnetooptical effects on properties of surface modes in one dimensional magnetized plasma photonic crystals
View Description Hide DescriptionWe have studied the properties of surface modes on one dimensional magnetized plasma photonic crystals in two configurations: Faraday and Voigt configurations. The results have been demonstrated by using the transfer matrix method and employing boundary conditions for TE and TM modes, respectively. For the Voigt effect, only the TM mode is considered because the TE modes under the influence of external magnetic field have the same properties as unmagnetized plasma. The influence of external magnetic field has been studied for three cases, i.e., TE left circular polarization, TE right circular polarization, and TM surface modes. It is shown that the properties of surface modes can be tuned correspondingly by changing the cap layer thickness, wave vector, and external magnetic field in the desired photonic band gap. The results show that collision frequency has a negligible effect on surface modes. A new type of wave called Fano mode has been reported for the Voigt effect for the TM mode in the first band gap. Proof of its existence has been demonstrated in the present paper.

Phase mixing of relativistically intense longitudinal wave packets in a cold plasma
View Description Hide DescriptionPhase mixing of relativistically intense longitudinal wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically using the Dawson Sheet Model. A general expression for phase mixing time () as a function of amplitude of the wave packet (δ) and width of the spectrum () has been derived. It is found that the phase mixing time crucially depends on the relative magnitude of amplitude “δ” and the spectral width “”. For scales with δ as , whereas for scales with δ as , where ωp is the nonrelativistic plasma frequency and c is the speed of light in vacuum. We have also verified the above theoretical scalings using numerical simulations based on the Dawson Sheet Model.

Fast, hot electron production and ion acceleration in a helicon inductive plasma
View Description Hide DescriptionA large, timeaveraged, double layerlike plasma potential drop of 80 V over several hundred Debye lengths has been observed in the magnetic expansion region on the Madison Helicon eXperiment. It is operated in an inductive mode at 900 W and low argon operating pressures (0.12–0.20 mTorr) in the collisionless regime. The plasma space potential drop is due to the formation of a double layerlike structure in the magnetic expansion region and is much higher than the potential drop caused by a Boltzmann expansion. With the plasma potential drop, a locally negative potential ion hole region at lower pressures with a higher electron density than ion density has been observed just the downstream of the potential drop region. Twotemperature Maxwellian electron distributions with a warm ( eV) and bulk ( eV) components are observed just upstream of the double layer validated through a RF compensated Langmuir probe and an optical emission spectroscopy (OES) diagnostics. In the expansion chamber downstream of the double layerlike potential drop, a single warm ( eV) Maxwellian electron distribution is observed via both the Langmuir probe and OES diagnostics. Ion beam energies of 65 eV are also observed downstream of the potential drop.

Interactions of electrons with two lower hybrid waves
View Description Hide DescriptionThe effects of perturbed orbits on the interactions of electrons with two lower hybrid waves, one of which is resonant with electrons at a low phase velocity (vp1 = 3.8Vthe, where vp1 is the wave phase velocity and Vthe is the electron thermal speed) while the other is offresonant at a high phase velocity (vp2 = 5.5Vthe), have been studied by using the particle simulation code based on the gyrokinetic electron and fullykinetic ion (GeFi) model [Lin et al., Plasma Phys. Controlled Fusion 47, 657 (2005)]. When the amplitude of the offresonant wave is sufficiently small so that the resonances of these two waves do not overlap, the variation of the resonant wave amplitude is similar to that predicted by O'Neil's theory [O'Neil, Plasma Fluid 8, 12 (1965)]. With the increasing amplitude, the two resonances overlap and large scale chaos emerges. As a result, the damping of the resonant wave can be enhanced, which is due to that the trapped electron orbits are significantly perturbed by the offresonant wave. The diffusion process gives rise to the enhanced damping. When the overlap is sufficiently large, the damping of the offresonant wave and the oscillatory behavior of the wave amplitude are observed. In addition, the resonant plateau in the distribution function can be broadened due to the change in the chaotic region boundaries as the electron perturbed orbits are taken into account.

Theory on bright and dark soliton formation in strongly magnetized plasmas
View Description Hide DescriptionThe existence and properties of bright and dark solitons in strongly magnetized warm plasmas are investigated analytically. These solitons are solutions to a fourdimensional Hamiltonian system with zero and nonzero boundary conditions. Based on the dynamical systems theory, the parametric domains of magnetic field and soliton frequency for the existence of bright and dark solitons in both cold and warm plasmas are identified. It is found that the temperature effects play an important role in determining the parametric domains and properties of the solitons. Specifically, the temperature effects make it possible for the existence of multihump dark solitons and remove the constraint on magnetic field and soliton frequency caused by the nonnegative condition of the density profile. The numerical integration of the soliton equations shows that the bright soliton amplitude increases with magnetic field while the dark soliton amplitude decreases with it. For both bright and dark solitons, the temperature effects suppress the soliton amplitude.