scholarly journals Nonlinear Landau Damping of Alfven Waves and the Production and Propagation of Cosmic Rays

1981 ◽  
Vol 94 ◽  
pp. 255-256
Author(s):  
R. J. Stoneham
Keyword(s):  
Cosmic Rays ◽  
Phase Speed ◽  
Alfven Waves ◽  
Magnetized Plasma ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Fermi Acceleration ◽  
Image Position ◽  
Hydromagnetic Waves ◽  
The Waves

The existence of hydromagnetic waves (waves whose frequency ω is less than the ion gyrofrequency Ωi = eB/mic) in a collisionless magnetized plasma with β, the ratio of plasma pressure to magnetic pressure, much greater than unity is required in theories for Fermi acceleration of cosmic rays by converging scattering centres at a shock front, in theories for the adiabatic cooling of cosmic rays due to trapping by plasma instabilities in an expanding supernova remnant (Kulsrud and Zweibel 1975, Schwartz and Skilling 1978) and in theories for resonant scattering of cosmic rays by hydromagnetic waves in the hot phase of the interstellar medium (Holman et al. 1979). Hydromagnetic waves may be damped by thermal ion cyclotron damping for wavenumbers k≳Ωi/vi, where vi = (Ti/mi)1/2 is the average thermal ion speed, and by linear Landau damping for non-zero angles of propagation with respect to the ambient magnetic field (Foote and Kulsrud 1979). Damping by both these processes is strong in a high-β plasma where there are many particles travelling at the phase speed of the waves. Hydromagnetic waves propagating along may be damped by nonlinear wave-particle interactions, the most important of which is thermal ion Landau damping of the beat wave of two Alfvén waves. This nonlinear process has the effect of transferring energy from the waves to the particles and can therefore be considered as a damping process for the waves.

scholarly journals Evolution of Supernova Remnants with Cosmic Rays and Radiative Cooling

1994 ◽  
Vol 142 ◽  
pp. 841-844
Author(s):  
E. A. Dorfi
Keyword(s):  
Cosmic Rays ◽  
Thermal Plasma ◽  
Supernova Remnants ◽  
Numerical Models ◽  
High Energy ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Radiative Cooling ◽  
Fermi Acceleration ◽  
Wave Heating

AbstractRecent numerical models for SNR evolution are presented, including first-order Fermi acceleration with injection of suprathermal particles at the shock wave, heating due to dissipation of Alfvén waves in the precursor region and radiative cooling of the thermal plasma. The X-ray fluxes obtained from these SNR models show significant differences depending on the acceleration efficiency of cosmic rays. γ-ray fluxes are calculated originating from π0-decay of pions generated by collisions of the high-energy particles with the thermal plasma. Cooling of the thermal plasma and dissipation of Alfvén waves in the precursor are important to determine the final amount of the explosion energy ESN which is transferred into cosmic rays.Subject headings: acceleration of particles — cosmic rays — gamma rays: theory — shock waves — supernova remnants

A Discussion on the early days of ionospheric research and the theory of electric and magnetic waves in the ionosphere and magnetosphere - Waves in a hot plasma

1975 ◽  
Vol 280 (1293) ◽  
pp. 95-110 ◽  
Keyword(s):  
Cyclotron Frequency ◽  
Phase Speed ◽  
Direct Application ◽  
Magnetized Plasma ◽  
Landau Damping ◽  
Unperturbed Motion ◽  
Hot Plasma ◽  
New Phenomena ◽  
The Waves ◽  
Thermal Speed

In studying wave propagation in a hot plasma, we treat the dynamics of the medium by kinetic theory rather than by continuum mechanics. The theory thus combines Maxwell’s equations with a transport equation in phase space (the Vlasov equation). An outline of the required procedure will be given. Some of the results are in close agreement with those of the fluid treatment provided the specific heat ratio is appropriately chosen. This is generally the case if the phase speed of the waves well exceeds the thermal speed of the electrons and, for a magnetized plasma, the frequency is not close to a harmonic of the cyclotron frequency. New phenomena are found if there are particles whose unperturbed motion is in resonance with the wave field. In the unmagnetized case this results in Landau damping or in instabilities, the latter being analogous to the mechanism of the laser. In the magnetized case there are, in addition, completely new modes of propagation for waves travelling approximately normal to the applied field. Many of these phenomena find direct application in ionospheric phenomena and diagnostics.

scholarly journals Spatially localized particle energization by Landau damping in current sheets produced by strong Alfvén wave collisions

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
Gregory G. Howes ◽  
Andrew J. McCubbin ◽  
Kristopher G. Klein
Keyword(s):  
Alfven Waves ◽  
Magnetized Plasma ◽  
Alfven Wave ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Correlation Technique ◽  
Nonlinear Simulation ◽  
Current Sheets ◽  
Strongly Nonlinear ◽  
Particle Energization

Understanding the removal of energy from turbulent fluctuations in a magnetized plasma and the consequent energization of the constituent plasma particles is a major goal of heliophysics and astrophysics. Previous work has shown that nonlinear interactions among counterpropagating Alfvén waves – or Alfvén wave collisions – are the fundamental building block of astrophysical plasma turbulence and naturally generate current sheets in the strongly nonlinear limit. A nonlinear gyrokinetic simulation of a strong Alfvén wave collision is used to examine the damping of the electromagnetic fluctuations and the associated energization of particles that occurs in self-consistently generated current sheets. A simple model explains the flow of energy due to the collisionless damping and the associated particle energization, as well as the subsequent thermalization of the particle energy by collisions. The net particle energization by the parallel electric field is shown to be spatially localized, and the nonlinear evolution is essential in enabling spatial non-uniformity. Using the recently developed field–particle correlation technique, we show that particles resonant with the Alfvén waves in the simulation dominate the energy transfer, demonstrating conclusively that Landau damping plays a key role in the spatially localized damping of the electromagnetic fluctuations and consequent energization of the particles in this strongly nonlinear simulation.

scholarly journals Dynamics of Alfvén waves in the night-side ionospheric Alfvén resonator at mid-latitudes

2005 ◽  
Vol 23 (2) ◽  
pp. 499-507 ◽  
Author(s):  
V. V. Alpatov ◽  
M. G. Deminov ◽  
D. S. Faermark ◽  
I. A. Grebnev ◽  
M. J. Kosch
Keyword(s):  
Pulse Duration ◽  
Alfven Waves ◽  
Fundamental Period ◽  
Alfvén Waves ◽  
Shear Mode ◽  
Q Factor ◽  
Trapped Waves ◽  
Alfven Resonator ◽  
Ionospheric Alfven Resonator ◽  
The Waves

Abstract. A numerical solution of the problem on dynamics of shear-mode Alfvén waves in the ionospheric Alfvén resonator (IAR) region at middle latitudes at nighttime is presented for a case when a source emits a single pulse of duration τ into the resonator region. It is obtained that a part of the pulse energy is trapped by the IAR. As a result, there occur Alfvén waves trapped by the resonator which are being damped. It is established that the amplitude of the trapped waves depends essentially on the emitted pulse duration τ and it is maximum at τ=(3/4)T, where T is the IAR fundamental period. The maximum amplitude of these waves does not exceed 30% of the initial pulse even under optimum conditions. Relatively low efficiency of trapping the shear-mode Alfvén waves is caused by a difference between the optimum duration of the pulse and the fundamental period of the resonator. The period of oscillations of the trapped waves is approximately equal to T, irrespective of the pulse duration τ. The characteristic time of damping of the trapped waves τdec is proportional to T, therefore the resonator Q-factor for such waves is independent of T. For a periodic source the amplitude-frequency characteristic of the IAR has a local minimum at the frequency π/ω=(3/4)T, and the waves of such frequency do not accumulate energy in the resonator region. At the fundamental frequency ω=2π/T the amplitude of the waves coming from the periodic source can be amplified in the resonator region by more than 50%. This alone is a basic difference between efficiencies of pulse and periodic sources of Alfvén waves. Explicit dependences of the IAR characteristics (T, τdec, Q-factor and eigenfrequencies) on the altitudinal distribution of Alfvén velocity are presented which are analytical approximations of numerical results.

scholarly journals Investigating the damping rate of phase-mixed Alfvén waves

2019 ◽  
Vol 632 ◽  
pp. A93 ◽  
Author(s):  
A. P. K. Prokopyszyn ◽  
A. W. Hood
Keyword(s):  
Wave Energy ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Coronal Loops ◽  
Phase Mixing ◽  
Heating Mechanism ◽  
At Resonance ◽  
Damping Rate ◽  
Field Lines ◽  
The Waves

Context. This paper investigates the effectiveness of phase mixing as a coronal heating mechanism. A key quantity is the wave damping rate, γ, defined as the ratio of the heating rate to the wave energy. Aims. We investigate whether or not laminar phase-mixed Alfvén waves can have a large enough value of γ to heat the corona. We also investigate the degree to which the γ of standing Alfvén waves which have reached steady-state can be approximated with a relatively simple equation. Further foci of this study are the cause of the reduction of γ in response to leakage of waves out of a loop, the quantity of this reduction, and how increasing the number of excited harmonics affects γ. Methods. We calculated an upper bound for γ and compared this with the γ required to heat the corona. Analytic results were verified numerically. Results. We find that at observed frequencies γ is too small to heat the corona by approximately three orders of magnitude. Therefore, we believe that laminar phase mixing is not a viable stand-alone heating mechanism for coronal loops. To arrive at this conclusion, several assumptions were made. The assumptions are discussed in Sect. 2. A key assumption is that we model the waves as strictly laminar. We show that γ is largest at resonance. Equation (37) provides a good estimate for the damping rate (within approximately 10% accuracy) for resonant field lines. However, away from resonance, the equation provides a poor estimate, predicting γ to be orders of magnitude too large. We find that leakage acts to reduce γ but plays a negligible role if γ is of the order required to heat the corona. If the wave energy follows a power spectrum with slope −5/3 then γ grows logarithmically with the number of excited harmonics. If the number of excited harmonics is increased by much more than 100, then the heating is mainly caused by gradients that are parallel to the field rather than perpendicular to it. Therefore, in this case, the system is not heated mainly by phase mixing.

Linear kinetic Alfvén waves in inhomogeneous plasma: Effects of Landau damping

2016 ◽  
Vol 113 (2) ◽  
pp. 25001 ◽  
Author(s):  
R. P. Sharma ◽  
R. Goyal ◽  
Nidhi Gaur ◽  
Earl E. Scime
Keyword(s):  
Inhomogeneous Plasma ◽  
Alfven Waves ◽  
Landau Damping ◽  
Alfvén Waves ◽  
Plasma Effects ◽  
Linear Kinetic ◽  
Kinetic Alfvén Waves

scholarly journals Properties of Alfvén Solitons in a Finite-Beta Plasma J. Plasma Phys. vol. 27, 1982, p. 193

1984 ◽  
Vol 32 (2) ◽  
pp. 347-347 ◽  
Author(s):  
Steven R. Spangler ◽  
James P. Sheerin
Keyword(s):  
Soliton Solutions ◽  
Alfven Waves ◽  
Plasma Phys ◽  
Alfvén Waves ◽  
Envelope Soliton ◽  
Translational Invariance ◽  
Non Linear ◽  
Image Position

In the aforementioned paper we obtained an equation for non-linear Alfvén waves in a finite-β plasma, and investigated envelope soliton solutions thereof. The purpose of this note is to point out an error in the derivation of the soliton envelopes, and present corrected expressions for these solitons.The error arises from our assumption of translational invariance of both the envelope and phase of an envelope soliton expressed in equations (16) and (17). Rather, the phase is related to the amplitude by where y ≡ x — VEt is a comoving co-ordinate, and all other quantities are defined in the above paper.

Nonlinear Landau Damping of Alfvén Waves in a High β Plasma

1982 ◽  
Vol 37 (8) ◽  
pp. 809-815 ◽  
Author(s):  
Heinrich J. Völk ◽  
Catherine J. Cesarsky
Keyword(s):  
Wave Length ◽  
Wave Spectrum ◽  
Nonlinear Damping ◽  
Alfven Waves ◽  
Alfvén Waves ◽  
Propagating Waves ◽  
Damping Rate ◽  
Nonlinear Landau Damping ◽  
The Waves ◽  
The Magnetic Field

A study is made of the nonlinear damping of parallel propagating Alfvén waves in a high β plasma. Two circularly polarized parallel propagating waves give rise to a beat wave, which in general contains both a longitudinal electric field component and a longitudinal gradient in the magnetic field strength. The wave damping is due to the interactions of thermal particles with these fields. If the amplitudes of the waves are low, a given wave (ω1, k1) is damped by the presence of all longer wavelength waves; thus, if the amplitudes of the waves in the wave spectrum increase with wave length, the effect of the longest waves is dominant.However, when the amplitude of the waves is sufficiently high, the particles are trapped in the wave packets, and the damping rate may be considerably reduced. We calculate the induced electrostatic field, and examine the trapping of thermal particles in a pair of waves. Finally, we give examples of modified damping rates of a wave in the presence of a spectrum of waves, and show that, when the trapping is effective, the waves are mostly damped by their interactions with waves of comparable wavelengths

Secondary flow due to Alfvén waves

1977 ◽  
Vol 80 (1) ◽  
pp. 179-202 ◽  
Author(s):  
J. A. Shercliff
Keyword(s):  
Hyperbolic Equations ◽  
Wave Mode ◽  
Alfven Waves ◽  
Secondary Flows ◽  
Alfvén Waves ◽  
Stored Energy ◽  
Axial Field ◽  
Electromagnetic Characteristics ◽  
The Waves ◽  
Made In

Large (gigajoule) amounts of energy can in principle be stored as kinetic energy in liquid metal circulating round a torus and can be extracted at the gigawatt level by Alfvén waves propagating along an imposed axial field. A major limitation on the energy that may be so stored is the disruption of these primary Alfvén waves by secondary flows in meridional planes, associated with out-of-balance centrifugal forces ahead of and behind the waves and non-uniform magnetic pressures at the wave fronts. Vorticity, created at the wave, itself propagates in secondary Alfvén waves.This paper gives a linearized treatment of these secondary motions and the associated perturbations of the imposed axial field and compares the resulting disruption of the primary wave mode with crude estimates made in an earlier paper. The main case treated is the discharge of the stored energy into a matched resistor by an Alfvén step wave but the secondary consequences of standing primary waves are also explored. The nature of the solutions depends on the electromagnetic characteristics of the walls normal to the imposed field. The problem is mathematically interesting because it involves the joint solving of elliptic and hyperbolic equations that are coupled by the boundary conditions at these walls.

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