Volume 18, Issue 1, January 2011

A fireball is formed inside a highly transparent spherical grid immersed in a dc discharge plasma. The ambient plasma acts as a cathode and the positively biased grid as an anode. A strong nearly currentfree double layer separates the two plasmas.Electrons are accelerated into the fireball, ionize, and establish a discharge plasma with plasma potential near the grid potential. Ions are ejected from the fireball. Since electrons are lost at the same rate as ions, most electrons accelerated into the fireball just pass through it. Thus, the electron distribution contains radially counterstreaming electrons. Highfrequency oscillations are excited with rf period given by the electrontransit time through the fireball. Since the frequency is well below the electronplasma frequency, no eigenmodes other than a beam spacecharge wave exists. The instability is an inertial transittime instability similar to the sheathplasma instability or the reflex vircator instability. In contrast to vircators, there is no electron reflection from a spacecharge layer but counterstreaming arises from spherical convergence and divergence of electrons. While the basic instability properties have been presented in a companion paper [R. L. Stenzel et al., Phys. Plasmas18, 012104 (2011)], the present paper focuses on observed mode jumping and nonlinear effects. The former produce frequency jumps and different potential profiles, the latter produce harmonics associated with electron bunching at large amplitudes. In situ probe measurements are presented and interpreted.
 ANNOUNCEMENTS


Announcement: The 2010 James Clerk Maxwell Prize for Plasma Physics
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 LETTERS


Model experiment of cosmic ray acceleration due to an incoherent wakefield induced by an intense laser pulse
View Description Hide DescriptionThe first report on a model experiment of cosmic ray acceleration by using intense laser pulses is presented. Large amplitude light waves are considered to be excited in the upstream regions of relativistic astrophysical shocks and the wakefield acceleration of cosmic rays can take place. By substituting an intense laser pulse for the large amplitude light waves, such shock environments were modeled in a laboratory plasma. A plasma tube, which is created by imploding a hollow polystyrene cylinder, was irradiated by an intense laser pulse. Nonthermal electrons were generated by the wakefield acceleration and the energy distribution functions of the electrons have a powerlaw component with an index of . The maximum attainable energy of the electrons in the experiment is discussed by a simple analytic model. In the incoherent wakefield the maximum energy can be much larger than one in the coherent field due to the momentum space diffusion or the energy diffusion of electrons.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Instability conditions and maximum growth rate of aperiodic instabilities
View Description Hide DescriptionThree linear kinetic plasma instabilities are investigated for a counterstreaming Maxwelliandistribution function with anisotropic temperatures such that aperiodic modes are generated. Concentration is focused on the instability condition, which is characterized by the marginally positive growth rate, and on the maximum growth rate and the associated fastest growing wavenumber. It is demonstrated that the simultaneous numerical solution of the dispersion relation and its derivative facilitates parameter studies for quantities such as the temperature anisotropy, thermal and streaming velocities, and the background magnetic field strength. Similarities and differences in the behavior of the three aperiodic modes are exemplified and implications for applications such as numerical simulations are illustrated.

Interlocking and nonlinear saturation of double tearing modes in differentially rotating plasmas
View Description Hide DescriptionInterlocking and nonlinear saturation of double tearing modes(DTMs) in rotating plasmas are investigated in a reduced magnetohydrodynamic model. Differential plasma rotation is found to have a significant stabilizing effect on the DTM. Analysis for the threshold island width and locking frequency is carried out. The effect of the viscosity on the mode is also discussed.

Spontaneously growing, weakly propagating, transverse fluctuations in anisotropic magnetized thermal plasmas
View Description Hide DescriptionA new dispersion formalism describing the weakly propagating, transverse fluctuations with wave vectors parallel to the uniform background magnetic field in an anisotropic biMaxwellian magnetized electronproton plasma is presented. Different transverse righthanded or lefthanded polarized modes can be excited, which are the whistler Weibellike modes and the electron and proton firehose modes. Analytic instability threshold conditions are derived in terms of the combined temperatureanisotropy, the parallel plasma beta , and the electron plasma frequency phase speed .

Transit time instabilities in an inverted fireball. I. Basic properties
View Description Hide DescriptionA new fireball configuration has been developed which produces vircatorlike instabilities. Electrons are injected through a transparent anode into a spherical plasma volume. Strong highfrequency oscillations with period corresponding to the electron transit time through the sphere are observed. The frequency is below the electron plasma frequency, hence does not involve plasmaeigenmodes. The sphere does not support electromagnetic eigenmodes at the instability frequency. However, the rf oscillations on the gridded anode create electron bunches which reinforce the grid oscillation after one transit time or rf period, which leads to an absolute instability. Various properties of the instability are demonstrated and differences to the sheathplasma instability are pointed out, one of which is a relatively high conversion efficiency from dc to rf power. Nonlinear effects are described in a companion paper [R. L. Stenzel et al., Phys. Plasmas18, 012105 (2011)].

Transit time instabilities in an inverted fireball. II. Mode jumping and nonlinearities
View Description Hide DescriptionA fireball is formed inside a highly transparent spherical grid immersed in a dc discharge plasma. The ambient plasma acts as a cathode and the positively biased grid as an anode. A strong nearly currentfree double layer separates the two plasmas.Electrons are accelerated into the fireball, ionize, and establish a discharge plasma with plasma potential near the grid potential. Ions are ejected from the fireball. Since electrons are lost at the same rate as ions, most electrons accelerated into the fireball just pass through it. Thus, the electron distribution contains radially counterstreaming electrons. Highfrequency oscillations are excited with rf period given by the electrontransit time through the fireball. Since the frequency is well below the electronplasma frequency, no eigenmodes other than a beam spacecharge wave exists. The instability is an inertial transittime instability similar to the sheathplasma instability or the reflex vircator instability. In contrast to vircators, there is no electron reflection from a spacecharge layer but counterstreaming arises from spherical convergence and divergence of electrons. While the basic instability properties have been presented in a companion paper [R. L. Stenzel et al., Phys. Plasmas18, 012104 (2011)], the present paper focuses on observed mode jumping and nonlinear effects. The former produce frequency jumps and different potential profiles, the latter produce harmonics associated with electron bunching at large amplitudes. In situ probe measurements are presented and interpreted.

Amplitude modulation of electron plasma waves in a quantum plasma
View Description Hide DescriptionUsing the one dimensional quantum hydrodynamic model for a twocomponent electronion dense quantum plasma the linear and nonlinear properties of electron plasma waves are studied including ion motion. By using the standard method of multiple scales perturbation technique a nonlinear Schrödinger equation containing quantum effects is derived. From this equation it is shown that with immobile ions an electron plasma wave becomes modulationally unstable in two distinct regions of the wavenumber. Numerical calculation shows that the stability domain of the wavevector shrinks with the increase in quantum diffraction effect. It is also found that the growth rate of instability in the high wavenumber region increases with the increase in quantum effect. Ion motion is found to have significant effect in changing the stability/instability domains of the wavenumber in the low region.

A hydrodynamical model for relativistic spin quantum plasmas
View Description Hide DescriptionBased on the onebody particleantiparticle Dirac theory of electrons, a set of relativistic quantum fluidequations for a spin half plasma is derived. The particleantiparticle nature of the relativistic particles is explicit in this fluid theory, which also includes quantum effects such as spin. The nonrelativistic limit is shown to be in agreement with previous attempts to develop a spin plasma theory derived from the Pauli Hamiltonian. Harnessing the formalism to the study of electromagnetic mode propagation, conceptually new phenomena are revealed; the particleantiparticle effects increase the fluid opacity to these waves, while the spin effects tend to make the fluid more transparent.

The plasma wave echo revisited
View Description Hide DescriptionTemporal plasma wave echoes are investigated by solving the Vlasov–Poisson system numerically in detail. The time of appearance and the structure of the echoes, including that of the higher harmonics and the dependence on the time between the excitations, are found to agree well with that from theory and/or experiments. Although Landau damping strongly depends on the small number of inphase (with the excited plasma waves)electrons, the latter do not noticeably affect echo formation even after they become trapped in the small but finite wave field. As expected, when one or both of the excitations become too strong, the number of trapped particles can become so large that the plasma echo ceases to exist.

Territorial characteristics of low frequency electrostatic fluctuations in a simple magnetized torus
View Description Hide DescriptionThis paper presents an experimental investigation of turbulence in simple toroidal plasma devices without rotational transform. It is argued that Rayleigh–Taylor (flute interchange) mode may be one of the source mechanisms for the observed turbulence but is not sufficient to explain its observed global characteristics. Taking BETA device as an example, we show that pure Rayleigh–Taylor mode cannot explain (i) the observation of mode maximum at the location other than where density scale length is minimum, (ii) the comparable value of amplitude level of fluctuations in good curvature region, and (iii) the decrease in the mode amplitude with increasing magnetic field. Investigations have revealed that there exists not only poloidal plasma flow but also that it is sheared. Including this effect explains the first observation. However, modification brought about by velocity shear in the Rayleigh–Taylor mode still does not explain our second and third observations. We have taken an approach that since Rayleigh–Taylor is not excited in a good curvature region, it cannot be the source of turbulence there. Nor is it defensible to say that turbulence born in a bad curvature region is carried over through rotation to the good curvature region. Consequently, we have invoked crossfield Simon–Hoh instability for this region. Experimental evidence supporting our proposal is presented. This paper concludes that toroidal devices have simultaneous existence of different selfconsistent sources of turbulence in different regions of the device.

Stabilization of ion temperature gradient driven instability by a vortex flow
View Description Hide DescriptionStabilization of ion temperature gradient(ITG) driven mode by a largescale vortexflow is investigated using a gyrofluid model in slab geometry. Extending a recent work [Z. X. Wang et al., Phys. Rev. Lett.103, 015004 (2009)], the focus in this work is put on the effect of magnetic shear. It is shown that the vortexflow can effectively stabilize the ITGmode by inducing both radial and poloidal mode couplings. Furthermore, decreasing magnetic shear is identified to weaken the stabilizing role of the vortexflow. The effects of the magnetic shear on the ITGmode structure and on the growth rate in the presence of various shear flows are obtained and the relevant mechanisms are discussed in detail.
 Nonlinear Phenomena, Turbulence, Transport

Nonlinear evolution of an arbitrary density perturbation in a cold homogeneous unmagnetized plasma
View Description Hide DescriptionAn exact and general analytical solution describing the nonlinear evolution of a large amplitude plasma oscillation initiated by an arbitrary density perturbation which can be expressed as a Fourier series in is found. This general solution is first used to reproduce the earlier results of R. C. Davidson and P. P. Schram [Nucl. Fusion8, 183 (1968)] and J. M. Dawson [Phys. Rev.113, 383 (1959)] using appropriate initial conditions and later applied to derive the space time evolution for a square wave and a triangular wave. It is found that the addition of a second harmonic increases the wave breaking limit of the fundamental mode. Analytical results pertaining to this two mode case have been verified using onedimensional particleincell simulation.

Damped eigenmode saturation in plasma fluid turbulence
View Description Hide DescriptionA broad sample of fluid models for instabilitydrivenplasma turbulence is surveyed to determine whether saturation involving damped eigenmodes requires special physics or is a common property of plasma turbulence driven by instability. Previous investigations have focused exclusively on turbulence in the core of tokamak discharges. The models surveyed here apply to a wide range of physical mechanisms for instability,turbulentmode coupling, and parameter regimes, with the common modeling feature that the physics has been reduced to a twofield fluid description. All the models have regimes in which damped eigenmodes saturate the instability by damping the fluctuation energy at a rate comparable to the injection rate by the unstable eigenmode. A test function derived from model parameters is found to predict when damped eigenmodes provide saturation. This confirms that a critical condition for saturation by damped eigenmodes is that the damping rate of the damped eigenmode does not greatly exceed the growth rate. For the quadratic dispersion relation of twofield models, this tends to hold in regimes of stronger instability and for regimes with strong gradients and strong diamagnetic frequency. Nonlinear coupling also matters. Strong coupling can overcome the effects of heavy damping, while weak coupling can prevent a damped eigenmode from saturating turbulence even though it is not heavily damped. This study indicates that damped eigenmodes represent a pervasive mechanism for the saturation of plasma instability in fluid descriptions, complementing recent works showing these effects in comprehensive gyrokinetic models.

Effects of parallel dynamics on vortex structures in electron temperature gradient driven turbulence
View Description Hide DescriptionVortex structures and related heat transport properties in slab electron temperature gradient (ETG) driven turbulence are comprehensively investigated by means of nonlinear gyrokinetic Vlasov simulations, with the aim of elucidating the underlying physical mechanisms of the transition from turbulent to coherent states. Numerical results show three different types of vortex structures, i.e., coherent vortex streets accompanied with the transport reduction, turbulentvortices with steady transport, and a zonalflowdominated state, depending on the relative magnitude of the parallel compression to the diamagnetic drift. In particular, the formation of coherent vortex streets is correlated with the strong generation of zonal flows for the cases with weak parallel compression, even though the maximum growth rate of linear ETG modes is relatively large. The zonal flow generation in the ETG turbulence is investigated by the modulational instability analysis with a truncated fluid model, where the parallel dynamics such as acoustic modes for electrons is incorporated. The modulational instability for zonal flows is found to be stabilized by the effect of the finite parallel compression. The theoretical analysis qualitatively agrees with secondary growth of zonal flows found in the slab ETG turbulence simulations, where the transition of vortex structures is observed.

Weakly relativistic solitons in a magnetized ionbeam plasma in presence of electron inertia
View Description Hide DescriptionThe relativistic compressive solitons of fast ionacoustic mode are established in this magnetized plasma for the introduction of relativistic beam when or subject to ( initial streaming, initial streaming, and is the beam drift perpendicular to the direction of magnetic field). The lighter concentration of beam ions in the plasma admits slower variation in amplitudes after some critical ( density) for all . Further, it is shown that under smaller relativistic effect ( and ) for small concentration of beam ions in the plasma, the growth of soliton amplitude becomes smaller with the increase of . But to the contrary, for heavier concentration of beam ions , the amplitudes of solitons decay considerably with growing sharply to a maximum in the vicinity of .

Reduced model simulations of the scrapeofflayer heatflux width and comparison with experiment
View Description Hide DescriptionReduced model simulations of turbulence in the edge and scrapeofflayer (SOL) region of a spherical torus or tokamak plasma are employed to address the physics of the scrapeofflayer heatflux width. The simulation model is an electrostatic twodimensional fluid turbulence model, applied in the plane perpendicular to the magnetic field at the outboard midplane of the torus. The model contains curvaturedriveninterchange modes, sheath losses, and both perpendicular turbulent diffusive and convective (blob) transport. These transport processes compete with classical parallel transport to set the SOL width. Midplane SOL profiles of density, temperature, and parallel heat flux are obtained from the simulation and compared with experimental results from the National Spherical Torus Experiment [S. M. Kaye et al. , Phys. Plasmas8, 1977 (2001)] to study the scaling of the heatflux width with power and plasma current. It is concluded that midplane turbulence is the main contributor to the SOL heatflux width for the low power Hmode discharges studied, while additional physics is required to fully explain the plasma current scaling of the SOL heatflux width observed experimentally in higher power discharges. Intermittent separatrixspanning convective cells are found to be the main mechanism that sets the nearSOL width in the simulations. The roles of sheared flows and blob trapping versus emission are discussed.

Impact of collisionality on fluctuation characteristics of microturbulence
View Description Hide DescriptionThe influence of changing collisionality on density fluctuation characteristics is studied during dedicated scaling experiments, using Doppler backscattering system. First, the repartition of fluctuation energy over different spatial scales, as represented by the wavenumber spectrum, is investigated and a modification of the shape of the perpendicular wavenumber spectrum in the low wavenumber part of the spectrum is observed when changing collisionality. In addition, a new procedure to evaluate the dispersion relation of microturbulence is presented. From the behavior of the perpendicular mean velocity of density fluctuations with the perpendicular wavenumber, different dispersion relations are obtained between low and high collisionality cases.

Linear and nonlinear Landau resonance of kinetic Alfvén waves: Consequences for electron distribution and wave spectrum in the solar wind
View Description Hide DescriptionKinetic Alfvén waveturbulence in solar wind is considered and it is shown that nonMaxwellian electron distribution function has a significant effect on the dynamics of solar wind plasmas. Linear Landau damping leads to the formation of a plateau in the parallel electron distribution function which diminishes the Landau damping rate significantly. Nonlinear scattering of waves by plasma particles is generalized to short wavelengths and it is found that for the solar wind parameters this scattering is the dominant process as compared to threewave decay and coalescence in the wave vector range . Incorporation of these effects leads to the steepening of the wave spectrum between the inertial and the dissipation ranges with a spectral index between 2 and 3. This region can be labeled as the scattering range. Such steepening has been observed in the solar wind plasmas.

Transport properties of hightemperature air in a magnetic field
View Description Hide DescriptionTransport properties of equilibrium air plasmas in a magnetic field are calculated with the Chapman–Enskog method. The range considered for the temperature is [50–50 000] K and for the magnetic induction is [0–300] T.