Whistler Pulse Research Articles

Laboratory Measurement of Large‐Amplitude Whistler Pulses Generated by Fast Magnetic Reconnection

AbstractWe present observations of large‐amplitude (δB/B∼ 0.01) oblique whistler wave pulses generated by a spontaneous, 3‐D localized magnetic reconnection event in the Caltech jet experiment. The wave pulses are measured more than 50 ion skin depths from the reconnection location by a tetrahedron array of three‐axis B‐dot probes that mimic the pyramid flight formations of the Cluster and Magnetospheric Multiscale Mission spacecraft. Measurements of background parameters, wave polarization, and wave dispersion confirm that the pulses are whistler modes. These results demonstrate that localized impulsive reconnection events can generate large‐amplitude, oblique whistler wave pulses that propagate far outside the reconnection region. This provides a new pathway for the generation of magnetospheric whistler pulses and may help explain relativistic particle acceleration in phenomena such as solar flares that incorporate 3‐D localized impulsive magnetic reconnection.

Conversion efficiency of even harmonics of whistler pulse in quantum magnetoplasma

AbstractStudy of even harmonic generation resulting from propagation of whistler pulse in homogeneous high-density quantum plasma immersed in an externally applied magnetic field, using the recently developed quantum hydrodynamic model is presented. The effects of quantum Bohm potential, quantum statistical pressure, and electron spin have been taken into account. The field amplitude of even harmonic of the whistler with respect to fundamental wave and the conversion efficiency for phase-mismatch has been analyzed. The conversion efficiency of harmonic radiation depends on the plasma electron density, magnetic field strength as well as the intensity of whistler pulse. The efficiency increases significantly with an increase in plasma density, magnetic field and whistler wave intensity. Higher conversion efficiency is observed in degenerate plasma for lower values of the static magnetic field as compared with classical plasma.

Propagation of a nonlinear wave packet driven in a relaxed magnetohydrodynamic plasma

We report the observation of a nonlinear wave packet propagating through a relaxed Taylor state in the Swarthmore Spheromak eXperiment (SSX) device. The wave packet is launched by a fast, pulsed, high current (${\approx}21~\text{kA}$) single-turn theta-pinch coil mounted outside the plasma vessel. The theta-pinch coil is energized by discharging a 40 kV, 2 kJ capacitor circuit. The wave packet velocity is super-thermal and super-Alfvénic; its group velocity is more consistent with a whistler pulse than other characteristic velocities. We also observe a fast density pulse which indicates that it is not Alfvénic in nature.

Electron acceleration by whistler pulse in high-density plasma

AbstractThe acceleration of an electron by the ponderomotive force of a Gaussian whistler pulse in a magnetized high-density quantum plasma obeying Fermi–Dirac distribution is studied using the recently developed quantum hydrodynamic model. Effective acceleration takes place when the peak whistler amplitude exceeds a threshold value, and the whistler frequency is greater than the cyclotron frequency. The threshold amplitude decreases with ratio of plasma frequency to electron cyclotron frequency. The electron is accelerated at velocities of about twice the group velocity of the whistler.

Magnetar activity mediated by plastic deformations of neutron star crust

We advance a "Solar flare" model of magnetar activity, whereas a slow evolution of the magnetic field in the upper crust, driven by electron MHD (EMHD) flows, twists the external magnetic flux tubes, producing persistent emission, bursts and flares. At the same time the neutron star crust plastically relieves the imposed magnetic field stress, limiting the strain $ \epsilon_t $ to values well below the critical strain $ \epsilon_{crit}$ of a brittle fracture, $ \epsilon_t \sim 10^{-2}\epsilon_{crit} $. Magnetar-like behavior, occurring near the magnetic equator, takes place in all neutron stars, but to a different extent. The persistent luminosity is proportional to cubic power of the magnetic field (at a given age), and hence is hardly observable in most rotationally powered neutron stars. Giant flares can occur only if the magnetic field exceeds some threshold value, while smaller bursts and flares may take place in relatively small magnetic fields. Bursts and flares are magnetospheric reconnection events that launch Alfven shocks which convert into high frequency whistlers upon hitting the neutron star surface. The resulting whistler pulse induces a strain that increases with depth both due to the increasing electron density (and the resulting slowing of the waves), and due to the increasing coherence of a whistler pulse with depth. The whistler pulse is dissipated on a time scale of approximately a day at shallow depths corresponding to $\rho \sim 10^{10} {\rm g cm}^{-3}$; this energy is detected as enhanced post-flare surface emission.

Ponderomotive acceleration of electrons by a whistler pulse

A Gaussian whistler pulse is shown to cause ponderomotive acceleration of electrons in a plasma when the peak whistler amplitude exceeds a threshold value and the whistler frequency is greater than half the cyclotron frequency, ω>ωc/2. The threshold amplitude decreases with the ratio of plasma frequency to electron cyclotron frequency, ωp/ωc. However, above the threshold amplitude, the acceleration energy decreases with ωp/ωc. The electrons gain velocities about twice the group velocity of the whistler.

Three-dimensional dynamics of nonlinear whistlers in plasmas

Recent satellite observations reveal localized whistler wavepackets that are correlated with density and magnetic field perturbations. This can be understood in terms of nonlinear interactions between three-dimensional whistlers and the background plasma density and magnetic field. The relevant equations for such nonlinear wave couplings are presented. Simulation studies of nonlinearly coupled electron whistlers and low-frequency magnetosonic perturbations reveal interesting features of whistler pulse compression and diffraction as well as the formation of magnetosonic wedges behind a three-dimensional (3D) localized whistler pulse. The results are useful for understanding the nonlinear propagation of whistlers in space and laboratory plasmas. We suggest that new experiments should be conducted to verify the 3D nonlinear wave phenomena involving electron whistlers and magnetosonic perturbations that we have described in here.

Pulsed currents carried by whistlers. VI. Nonlinear effects

In a large magnetized laboratory plasma (n≂1011 cm−3, kTe≥1 eV, B0≥10 G, 1 m × 2.5 m), current pulses in excess of the Langmuir limit (150 A, 0.2 μs) are drawn to electrodes in a parameter regime characterized by electron magnetohydrodynamics (ωci≪ω≪ωce). The transient plasma current is transported by low-frequency whistlers forming wave packets with topologies of three-dimensional vortices. The generalized vorticity, Ω, is shown to be frozen into the electron fluid drifting with velocity v, satisfying ∂Ω/∂t≂∇×(v×Ω). The nonlinearity in v×Ω is negligible since v and Ω(r,t) are found to be nearly parallel. However, large currents associated with v≥(2kTe/me)1/2 lead to strong electron heating which modifies the damping of whistlers in collisional plasmas. Heating in a flux tube provides a filament of high Spitzer conductivity, which permits a nearly collisionless propagation of whistler pulses. This filamentation effect is not associated with density modifications as in modulational instabilities, but arises from conductivity modifications. The companion paper [Stenzel and Urrutia, Phys. Plasmas 3, 2599 (1996)] shows that, after the decay of the transient wave magnetic field, magnetic helicity remains in the plasma due to temperature-gradient driven currents.

Nonlinear Phenomena Associated with Large Amplitude Whistler Pulses

In a magnetized laboratory plasma (n 10 11 cm -3 , kT e ≥ 1 eV, B 0 ≥ 10 G, 1 m diam x 2.5 m) large amplitude current pulses (150 A, 0.2 μs) are excited in the parameter regime described by Electron MHD (EMHD ; ω ci << ω << ω ce ). The currents are transported by low-frequency whistlers forming wave packets with topologies resembling 3D spherical vortices. The generalized vorticity, Ω = ⊇ x (v + eA/m e ), is shown to be frozen into the electron fluid, ∂Ω/∂t ⊇ x (v x Ω). The nonlinearity in v x Ω is negligible since v and Ω(r,t) are found to be nearly parallel. Thus, large amplitude pulses [Ω(r, t) ≤ Ω 0 = eB 0 /m e ] show the same behavior as small amplitude pulses. However, the associated large currents with v drift ≥ (kT e /me) 1/2 lead to strong electron heating which can modify the damping of whistlers in collisional plasmas (ω ∼ v ei T e -3/2 ). Observations show that a heated flux tube provides a filament of high Spitzer conductivity which permits a nearly collisionless propagation of whistler pulses. This filamentation effect is not associated with density modifications as in modulational instabilities but arises from conductivity modifications. The heated flux tube also generates a quasi-dc magnetic field driven by thermoelectric currents. These assume self-consistently a Taylor state with ⊇ x B kB.

Transport of time-varying plasma currents by whistler wave packets

In a large laboratory plasma the properties of time-varying current systems have been studied experimentally. The parameter regime of interest involves magnetized electrons and unmagnetized ions. In the laboratory complete measurements of three-dimensional, time-varying vector fields of the total current density are obtained from magnetic probe measurements. Pulsed currents are observed to propagate at the speed of whistler wave packets. Their field structure forms flux-rope-like configurations which are electromagnetically force-free. Moving sources induce eddy currents which excite waves and form Cerenkov-like whistler wings. The radiation patterns of moving magnetic antennas and electrodynamic tethers have been investigated. The current closure between tethered electrodes across B/sub 0/ has been mapped. Nonlinear effects of large-amplitude, antenna-launched whistler pulses have been observed. These involve a new modulational instability in which a channel of high conductivity is formed which permits the wave/currents to penetrate deeply into a collisional plasma.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Nonlinear penetration of whistler pulses into collisional plasmas via conductivity modifications.

A strong electromagnetic impulse (\ensuremath{\Delta}t\ensuremath{\simeq}0.2 \ensuremath{\mu}s) with central frequency in the whistler-wave regime is applied to a large laboratory plasma dominated by Coulomb collisions (${\ensuremath{\nu}}_{\mathit{e}\mathit{i}}$\ensuremath{\simeq}\ensuremath{\omega}\ensuremath{\ll}${\mathrm{\ensuremath{\omega}}}_{\mathit{c}\mathit{e}}$\ensuremath{\ll}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}\mathit{e}}$). Local electron heating at the antenna and transport along ${\mathit{B}}_{0}$ create a channel of high conductivity along which the whistler pulse penetrates with little damping. Because of its rapid temporal evolution, this new form of modulational instability does not involve ducting by density gradients which require ion time scales to develop.

Test particle correlation by a whistler wave in a nonuniform magnetic field

Computer simulations of the correlation in phase of test electrons in a monochromatic whistler wave propagating along a nonuniform external magnetic field are presented. The behavior of resonant electrons depends on an inhomogeneity ratio R, which defines the external field gradient in relation to the wave amplitude. In the case ‖R‖&amp;lt;1, where electron trapping is possible, a hole (or an island) of particles is found to occur in phase plots of the distribution function. This causes the appearance of a transverse current coherent with the wave, which is most intense for ‖R‖≲0.6. The significance of these results to magnetospheric propagation of a quasi-monochromatic whistler pulse is discussed.

Self‐distortion of a whistler pulse in a plasma

Following the technique used by Akhmanov et al. to solve the nonlinear wave equation, we have investigated the propagation of temporally and spatially gaussian whistler pulses in a plasma. In the linear case the temporal width of the pulse is enhanced (due to dispersion) at a distance R ˜ τ2v3g/(∂2ω/∂k2) whereas its size is enhanced (due to diffraction) over a length Rd ∼ 2kr20/(1 + ϵ+/ϵzz); τ, r0, k, vg, ϵ+, and ϵzz are the initial time width, size, wave vector, group velocity, and the components of the dielectric tensor of the plasma. In the case of a high‐power whistler, the ponderomotive nonlinearity causes self‐focusing (for all values of ω/ωc) of the whistler and results in severe distortion of the pulse shape.

The sideband instability of electrostatic waves in an inhomogeneous medium

The work deals with the resonant particle excitation of two electrostatic waves with closely spaced wave numbers, when there is an inhomogeneity present in the form of a spatially dependent wave number. Resonant particle behaviour in such a field is investigated and the resonant particle current is computed for a variety of cases. If the inhomogeneity is such that resonant particles see the wave numbers of the waves increasing, then it turns out that the wave of greatest wave number is preferentially amplified. If the gradient is reversed it is the opposite wave which grows. Thus when a narrow band electrostatic wave is subject to beam excitation, only one of the sideband waves is unstable. The theory is applied to the closely analogous problem of sideband formation in the case of triggering of VLF emissions by magnetospheric whistler pulses, and seems to account for much of the observed behaviour.

A theory of VLF emissions

The work attempts to give a theoretical explanation of the triggering of VLF emissions by magnetospheric whistler morse pulses. First studied is the behaviour of resonant particles in a whistler wave train in an inhomogeneous medium. It is found that second order resonant particles become stably trapped in the wave. After 1–2 trapping periods such particles dominate the resonant particle distribution function, and produce large currents that are readily estimated. The in phase component of current will produce growth rates about n times the linear value when particles have been trapped for n trapping periods. A detailed analysis shows that the reactive component of current is able to cause a steady change in wave frequency. Next a realistic zero order distribution function is selected, and the growth rates and rates of change of frequency are computed in a magnetospheric whistler pulse in the equatorial zone. These results permit a plausible description of the triggering process. Explanations are offered for a number of detailed features of the process. The theory seems to fit in well with observed numerical observations.