Drift Kinetic Energy Research Articles

Interplay between the non-resonant streaming instability and self-generated pressure anisotropies

ABSTRACT The non-thermal particles escaping from collision-less shocks into the surrounding medium can trigger a non-resonant streaming instability that converts parts of their drift kinetic energy into large amplitude magnetic field perturbations, and promote the confinement and acceleration of high energy cosmic rays. We present simulations of the instability using an hybrid-Particle-in-Cell approach including Monte Carlo collisions, and demonstrate that the development of the non-resonant mode is associated with important ion pressure anisotropies in the background plasma. Depending on the initial conditions, the anisotropies may act on the instability by lowering its growth and trigger secondary micro-instabilities. Introducing collisions with neutrals yield a strong reduction of the magnetic field amplification as predicted by linear fluid theory. In contrast, Coulomb collisions in fully ionized plasmas are found to mitigate the self-generated pressure anisotropies and promote the growth of the magnetic field.

Spectral transition of multiscale turbulence in the tokamak pedestal

The transition in the turbulence spectrum from ion-scale dominated regimes to multiscale transport regimes that couple ion and electron scales is studied with gyrokinetic simulations of turbulent transport. The simulations are based on DIII-D high-confinement mode (H-mode) plasma parameters in the tokamak pedestal. The transition is initiated by varying the ion temperature gradient. To our knowledge, no full multiscale simulations of pedestal-like transport have been done previously. The experimental parameters lie in a bifurcation region between the two regimes. At long wavelengths, a complex, ion-direction hybrid mode is the dominant linearly unstable drift wave, while an electron temperature gradient-driven mode is unstable at short wavelengths. In the transition from the multiscale branch to the ion-scale branch, the magnitude of the ion-scale poloidal wavenumber spectrum of the nonlinear turbulent energy flux increases and the magnitude of the high-wavenumber spectrum decreases. The decrease in the electron-scale transport is due to nonlinear mixing with ion-scale fluctuations and the ion-scale-driven zonal flows. A shift in the total energy associated with the fluctuating electrostatic potential intensity from dominantly drift kinetic energy in the multiscale regime to dominantly potential intensity in the ion-scale regime is well-correlated with the trend in the total energy flux.

Verification of neoclassical toroidal viscosity induced by energetic particles

The thermal particles contributed neoclassical toroidal viscosity (NTV) have been successfully developed and explored by many impressive works such as the study by Shaing et al. [Phys. Plasmas 10, 1443 (2003)] and Zhu et al. [Phys. Rev. Lett. 96, 225002 (2006)]. In this work, the scope of the NTV study is extended to explore the contribution of energetic particles (EPs) through both theory and experiments. In theory, the existence of the NTV torque due to the precessional drift resonance of trapped EPs is identified based on the equivalence between the NTV torque and the perturbed drift kinetic energy [J. Park, Phys. Plasmas 18, 110702 (2011)]. Toroidal modeling with the Magneto Resistive Spectrum - drift Kinetic code [Y. Liu, Phys. Plasmas 15, 112503 (2008)], based on this equivalence, indicates that trapped EPs can contribute a significant amount of the NTV torque. Meanwhile, this work also focuses on developing the dedicated DIII-D experiments in the presence of the n = 2 external magnetic perturbation to verify the EP induced NTV (EP-NTV) by measuring the change of the NTV torque while varying the angle and the voltage of the neutral beam injection. However, the developed experiments have been unable to create conditions necessary to clearly demonstrate the presence of EP-NTV. The main challenge is separating the resonant and non-resonant momentum transport responses in the plasma. The experience, gained from this study, can help the further exploration of EP-NTV in the future experiments.

Transient optical non-linearity in p-Si induced by a few cycle extreme THz field.

We study the impact of a few cycle extreme terahertz (THz) radiation (the field strength ETHz ∼1-15 MV/cm is well above the DC-field breakdown threshold) on a p-doped Si wafer. Pump-probe measurements of the second harmonic of a weak infrared probe were done at different THz field strengths. The second harmonic yield has an unusual temporal behavior and does not follow the common instantaneous response, ∝ETHz2. These findings were attributed to: (i) the lattice strain by the ponderomotive force of the extreme THz pulse at the maximal THz field strength below 6 MV/cm and (ii) the modulation of the THz field-induced impact ionization rate at the optical probe frequency (due to the modulation of the free carriers' drift kinetic energy from the probe field) at the THz field strength above 6-8 MV/cm.

On the growth of the thermally modified non-resonant streaming instability

ABSTRACT The cosmic rays non-resonant streaming instability is believed to be the source of substantial magnetic field amplification. In this work, we investigate the effects of the ambient plasma temperature on the instability and derive analytical expressions of its growth rate in the hot, demagnetized regime of interaction. To study its non-linear evolution, we perform hybrid-PIC simulations for a wide range of temperatures. We find that in the cold limit, about two-thirds of the cosmic rays drift kinetic energy is converted into magnetic energy. Increasing the temperature of the ambient plasma can substantially reduce the growth rate and the magnitude of the saturated magnetic field.

Particle-in-cell simulation of Buneman instability beyond quasilinear saturation

Spatio-temporal evolution of Buneman instability has been followed numerically till its quasilinear quenching and beyond, using an in-house developed electrostatic 1D particle-in-cell (PIC) simulation code. For different initial drift velocities and for a wide range of electron to ion mass ratios, the growth rate obtained from simulation agrees well with the numerical solution of the fourth order dispersion relation. Quasi-linear saturation of Buneman instability occurs when the ratio of electrostatic field energy density to initial electron drift kinetic energy density reaches up to a constant value, which, as predicted by Hirose [Plasma Phys. 20, 481 (1978)], is independent of initial electron drift velocity but varies with the electron to ion mass ratio (m/M) as ≈(m/M)1/3. This result stands verified in our simulations. The growth of the instability beyond the first saturation (quasilinear saturation) till its final saturation [Ishihara et al., PRL 44, 1404 (1980)] follows an algebraic scaling with time. In contrast to the quasilinear saturation, the ratio of final saturated electrostatic field energy density to initial kinetic energy density is relatively independent of the electron to ion mass ratio and is found from simulation to depend only on the initial drift velocity. Beyond the final saturation, electron phase space holes coupled to large amplitude ion solitary waves, a state known as coupled hole-soliton, have been identified in our simulations. The propagation characteristics (amplitude–speed relation) of these coherent modes, as measured from present simulation, are found to be consistent with the theory of Saeki et al. [PRL 80, 1224 (1998)]. Our studies thus represent the first extensive quantitative comparison between PIC simulation and the fluid/kinetic model of Buneman instability.

Phosphorylation of rat brain purified mitochondrial Voltage-Dependent Anion Channel by c-Jun N-terminal kinase-3 modifies open-channel noise

The drift kinetic energy of ionic flow through single ion channels cause vibrations of the pore walls which are observed as open-state current fluctuations (open-channel noise) during single-channel recordings. Vibration of the pore wall leads to transitions among different conformational sub-states of the channel protein in the open-state. Open-channel noise analysis can provide important information about the different conformational sub-state transitions and how biochemical modifications of ion channels would affect their transport properties. It has been shown that c-Jun N-terminal kinase-3 (JNK3) becomes activated by phosphorylation in various neurodegenerative diseases and phosphorylates outer mitochondrion associated proteins leading to neuronal apoptosis. In our earlier work, JNK3 has been reported to phosphorylate purified rat brain mitochondrial voltage–dependent anion channel (VDAC) in vitro and modify its conductance and opening probability. In this article we have compared the open-state noise profile of the native and the JNK3 phosphorylated VDAC using Power Spectral Density vs frequency plots. Power spectral density analysis of open-state noise indicated power law with average slope value α ≈1 for native VDAC at both positive and negative voltage whereas average α value < 0.5 for JNK3 phosphorylated VDAC at both positive and negative voltage. It is proposed that 1/f1 power law in native VDAC open-state noise arises due to coupling of ionic transport and conformational sub-states transitions in open-state and this coupling is perturbed as a result of channel phosphorylation.

One dimensional PIC simulation of relativistic Buneman instability

Spatio-temporal evolution of the relativistic Buneman instability has been investigated in one dimension using an in-house developed particle-in-cell simulation code. Starting from the excitation of the instability, its evolution has been followed numerically till its quenching and beyond. The simulation results have been quantitatively compared with the fluid theory and are found to be in conformity with the well known fact that the maximum growth rate (γmax) reduces due to relativistic effects and varies with γe0 and m/M as γmax∼32γe0(m2M)1/3, where γe0 is the Lorentz factor associated with the initial electron drift velocity (v0) and (m/M) is the electron to ion mass ratio. Further it is observed that in contrast to the non-relativistic results [A. Hirose, Plasma Phys. 20, 481 (1978)] at the saturation point, the ratio of electrostatic field energy density (∑k|Ek|2/8π) to initial drift kinetic energy density (W0) scales with γe0 as ∼1/γe02. This novel result on the scaling of energy densities has been found to be in quantitative agreement with the scalings derived using fluid theory.

How important are the alpha‐proton relative drift and the electron heat flux for the proton heating of the solar wind in the inner heliosphere?

AbstractThis report explores the feasibility of explaining the observed proton heating in the inner heliosphere (1) by tapping the field‐aligned relative drift between alpha particles and protons in the solar wind plasma and (2) by tapping the strahl‐electron heat flux from the Sun. The observed reduction of the alpha‐proton drift kinetic energy from 0.3 to 1 AU and the observed reduction of electron heat flux from 0.3 to 1 AU are each about half of the energy needed to account for the observed heating of protons from 0.3 to 1 AU. A mechanism is identified to transfer the free energy of the alpha‐proton relative drift into proton thermal energy: the alpha‐proton magnetosonic instability. A mechanism is identified to transfer kinetic energy from the strahl‐electron heat flux into proton thermal energy: weak double layers. At the current state of knowledge, the plausibility of heating the solar wind protons via the alpha‐proton magnetosonic instability is high. The properties of the weak double layers that have been observed in the solar wind are not well known; more data analysis and plasma simulations are needed before the plausibility of heating the solar wind protons by the double‐layer mechanism can be evaluated.

Non-perturbative modelling of energetic particle effects on resistive wall mode: Anisotropy and finite orbit width

A non-perturbative magnetohydrodynamic-kinetic hybrid formulation is developed and implemented into the MARS-K code [Liu et al., Phys. Plasmas 15, 112503 (2008)] that takes into account the anisotropy and asymmetry [Graves et al., Nature Commun. 3, 624 (2012)] of the equilibrium distribution of energetic particles (EPs) in particle pitch angle space, as well as first order finite orbit width (FOW) corrections for both passing and trapped EPs. Anisotropic models, which affect both the adiabatic and non-adiabatic drift kinetic energy contributions, are implemented for both neutral beam injection and ion cyclotron resonant heating induced EPs. The first order FOW correction does not contribute to the precessional drift resonance of trapped particles, but generally remains finite for the bounce and transit resonance contributions, as well as for the adiabatic contributions from asymmetrically distributed passing particles. Numerical results for a 9MA steady state ITER plasma suggest that (i) both the anisotropy and FOW effects can be important for the resistive wall mode stability in ITER plasmas; and (ii) the non-perturbative approach predicts less kinetic stabilization of the mode, than the perturbative approach, in the presence of anisotropy and FOW effects for the EPs. The latter may partially be related to the modification of the eigenfunction of the mode by the drift kinetic effects.

Theory comparison and numerical benchmarking on neoclassical toroidal viscosity torque

Systematic comparison and numerical benchmarking have been successfully carried out among three different approaches of neoclassical toroidal viscosity (NTV) theory and the corresponding codes: IPEC-PENT is developed based on the combined NTV theory but without geometric simplifications [Park et al., Phys. Rev. Lett. 102, 065002 (2009)]; MARS-Q includes smoothly connected NTV formula [Shaing et al., Nucl. Fusion 50, 025022 (2010)] based on Shaing's analytic formulation in various collisionality regimes; MARS-K, originally computing the drift kinetic energy, is upgraded to compute the NTV torque based on the equivalence between drift kinetic energy and NTV torque [J.-K. Park, Phys. Plasma 18, 110702 (2011)]. The derivation and numerical results both indicate that the imaginary part of drift kinetic energy computed by MARS-K is equivalent to the NTV torque in IPEC-PENT. In the benchmark of precession resonance between MARS-Q and MARS-K/IPEC-PENT, the agreement and correlation between the connected NTV formula and the combined NTV theory in different collisionality regimes are shown for the first time. Additionally, both IPEC-PENT and MARS-K indicate the importance of the bounce harmonic resonance which can greatly enhance the NTV torque when E×B drift frequency reaches the bounce resonance condition.

The effects of plasma density and magnetic field on ion temperature and drift velocity in a LaB6 direct current plasma

In a LaB6 direct current plasma, parallel and perpendicular ion temperatures (Ti∥ and Ti⊥) were measured as a function of plasma density and magnetic field by a laser-induced fluorescence technique. In order to study the impacts of magnetic field and plasma density on ion temperature and drift velocity, the plasma density was controlled by a magnetic field and discharge current under the following plasma conditions: The magnetic field intensity at the measurement position, BD, was 186–405 G; discharge voltage, Vdis, was 29.9–32.1 V; discharge current, Idis, was 10–22 A; neutral pressures, Pn, were 130 mTorr (in the source region) and 2.2 mTorr (at diagnostic region); plasma density, np, was (2–8)×1012 cm−3; and electron temperature, Te, was ∼2.6 eV. Parallel ion temperature (Ti∥), perpendicular ion temperature (Ti⊥), and drift velocity, vD∥ (or drift kinetic energy, ED) all increase as a function of BD and Idis, such that the total ion energy, Et (=Ti⊥+Ti∥+ED), increases as a function of BD and Idis. From the relations of Ti∥, Ti⊥, and vD∥ to np, ion temperature and drift velocity were observed to be strongly depend on plasma density. In consideration of the collision time scales, ion gyrofrequency, and time of flight from the source to the measurement position, the dominant process for ion heating was observed to be the electron-ion collisions, although the magnetic field and ion-neutral collisions contribute to ion temperature anisotropy.

Magnetic drift kinetic damping of the resistive wall mode in large aspect ratio tokamaks

An analytical, large aspect ratio, calculation of the drift-kinetic energy perturbation is carried out for the resistive wall mode, due to the mode resonance with the magnetic precession drifts of trapped thermal ions and electrons. Four asymptotic cases are identified and analyzed in detail. Generally, a partial stabilization of the mode is possible thanks to the kinetic correction to the perturbed plasma energy. A complete stabilization can occur only in a narrow space of the plasma equilibrium parameters. Kinetic destabilization of the mode is also possible due to a finite pressure correction to the precession drift frequency.

Inertia and ion Landau damping of low-frequency magnetohydrodynamical modes in tokamaks

The inertia and Landau damping of low-frequency magnetohydrodynamical modes are investigated using the drift-kinetic energy principle for the motion along the magnetic field. Toroidal trapping of the ions decreases the Landau damping and increases the inertia for frequencies below (r/R)1/2vthi/qR. The theory is applied to toroidicity-induced Alfvén eigenmodes and to resistive wall modes in rotating plasmas. An explanation of the beta-induced Alfvén eigenmode is given in terms of the Pfirsch–Schlüter-like enhancement of inertia at low frequency. The toroidal inertia enhancement also increases the effects of plasma rotation on resistive wall modes.

Stimulated microwave emission from E x B drifting electrons in slow-wave cavities: A quantum approach.

Stimulated microwave emission from E\ifmmode\times\else\texttimes\fi{}B drifting electrons in slow-wave cavities occurs when the Doppler-shifted radiation frequency is either near zero or the electron cyclotron frequency. The former case, characterized by the synchronous drift velocity u, \ensuremath{\omega}-ku\ensuremath{\simeq}0, corresponds to the ``pure drift'' instability, while the latter, satisfying \ensuremath{\omega}-ku\ensuremath{\simeq}\ifmmode\pm\else\textpm\fi{}\ensuremath{\Omega}, is termed the ``drift-cyclotron'' mode. In both cases the drift kinetic energy and momentum are invariant during radiative transitions. The momentum of the emitted or absorbed radiation quantum comes from the vector potential associated with the static magnetic field and induces a shift of the electron guiding center in a direction transverse to the drift velocity. In the pure drift case the radiation energy comes from the change in the electrostatic potential energy. In the drift-cyclotron case both electrostatic and cyclotron rotation energies are converted into radiation. In the nonrelativistic regime the gain is symmetric with respect to the frequency detuning from resonance. The difference between the stimulated absorption and emission probabilities, responsible for the gain, is caused by field gradients across the direction of the electron drift. These gradients come from the waveguide mode structure and the collective field of the electron beam. The drift mode is always unstable, while there exists one stable and one unstable drift-cyclotron branch. Relativistic mass effects influence only the drift-cyclotron instability, adding a gain contribution that is antisymmetric in frequency detuning.

Nonlinear gain computation for the sheet beam crossed-field amplifier

When the RF amplitude in a crossed field device is much smaller than the external DC voltage, the energy exchange between an electron and the wave is given by the change in the potential energy of the electron guiding center. The shift of the beam center of charge follows the space bunching into spokes caused by the RF-induced drift. A nonlinear estimate for the gain is derived and applied to the linear format crossed-field amplifier fed by a continuous sheet beam. The adiabatic approximation for the guiding center trajectories in the low gain regime determines the fraction of trapped/streaming particles and the energy exchange for each group. The radiation gain equals the change in the electron potential energy resulting from the shift in the beam center of charge across the anode-cathode voltage. The drift kinetic energy is approximately conserved, opposed to other microwave devices converting kinetic energy into radiation. The theory accounts for the symmetry of the response curve relative to the frequency detuning /spl omega/-/spl omega//sub 0/, and the flat top near resonance. The analytic predictions agree with the experimental measurements of the gain versus frequency response. >

A magnetospheric critical velocity experiment: Particle results

In March of 1983, a barium injection sounding rocket experiment (the Star of Lima) was conducted to investigate Alfvén's critical ionization velocity (CIV) hypothesis in space. Included in the instrumented payload was a University of California, San Diego (UCSD), particle detection experiment consisting of five retarding potential analyzers. Despite conditions that appeared to be optimal for the critical velocity effect, the particle data, in agreement with optical observations, indicate that a fractional ionization of only ˜5×10−4 was observed, indicating that the conditions required for the effect to occur are still not well understood. However many of the required phenomena associated with the CIV effect were observed; in particular a superthermal electron population was formed at the expense of ion drift kinetic energy in the presence of intense electrostatic waves near the lower hybrid frequency. The amount of ionization produced is plausibly consistent with the observed electron flux, but could also be accounted for by residual solar UV at the injection point. It is shown based on the UCSD data set that one obvious explanation for the low ionization efficiency, namely that the ionizing superthermal electrons may rapidly escape along field lines, can be ruled out.

Computer simulations of electromagnetic cool ion beam instabilities

Electromagnetic instabilities driven by a relatively cool ion beam are studied by one‐dimensional hybrid computer simulations. Both the beam and the instabilities propagate parallel or antiparallel to a uniform magnetic field. At relatively small beam‐core relative drift speeds, similar to conditions predicted for ion beams upstream of slow shocks in the magnetotail, the right‐hand resonant instability exhibits quasi‐linear behavior. In particular, instability saturation is due to a reduction in the beam‐core relative drift speed as well as to an increase in the perpendicular‐to‐parallel beam temperature. For tenuous beams in this quasi‐linear regime the fluctuating magnetic field amplitude at saturation scales as the beam drift kinetic energy. At higher drift speeds, including parameters similar to those upstream of the quasi‐perpendicular bow shock, the right‐hand resonant and nonresonant instabilities both lead to phase bunching of the ion beam. The relative phase between the fluctuating velocity vector of the beam and the fluctuating magnetic field is examined; computed values agree with both linear theory during the early growth phase and nonlinear arguments at saturation. In this nonlinear regime both instabilities saturate when approximately half the initial beam drift kinetic energy density is converted to fluctuating magnetic field energy density.

Energy conservation and related constraints in drift wave turbulence

The problem of energy conservation for the renormalization of the drift wave instability in a sheared magnetic field is considered. It has been suggested previously that there is a connection between a certain constraint on the nonlinear term in the drift kinetic equation and energy conservation. Arguments are presented to dissolve this connection; and in turn, energy conservation is formulated in the physically meaningful statistically averaged sense. Finally, energy conservation is proven for the system of nonlinear equations, renormalized by the normal stochastic approximation, describing the drift wave instability.

Convective Cells in a Quiescent Plasma Region

Periodic spatial variations of density and potential were observed in the quiescent region of a plasma, in the magnetohydrodynamically stable region of a linear multipole. The variations were of the order of 50%, and were both radial and along the axial direction z, along which the magnetic field configuration was approximately invariant. Measurements of E/B velocities, as well as of particle flux, revealed drift velocities in closed vortices or convective cells, with the drift kinetic energy as high as 30% of the electron thermal energy. The cells persisted in the afterglow for at least a millisecond, roughly the plasma containment time. The axial dimension of the cells depended on the spatial variation of the input power density during ionization and heating; radially they extended from the stagnation point to near ψc [where ∂(§ dl/B)/∂ψ = 0], where there were large fluctuations of density and potential with time. The density in the quiescent region decayed at about the same rate as the density in the region of temporal fluctuations. The effect of convective cells on plasma loss is discussed.