Pitch angle scattering of an energetic magnetized particle by a circularly polarized electromagnetic wave

Pseudo Potential

The interaction between a circularly polarized electromagnetic wave and an energetic gyrating particle is described [1] using a relativistic pseudo-potential that is a function of the frequency mismatch,&#160; a measure of the extent to which &#969;-kzvz=&#937;/&#947; is not true. The description of this wave-particle interaction involves a sequence of relativistic transformations that ultimately demonstrate that the pseudo potential energy of a pseudo particle adds to a pseudo kinetic energy giving a total pseudo energy that is a constant of the motion. The pseudo kinetic energy is proportional to the square of the particle acceleration (compare to normal kinetic energy which is the square of a velocity) and the pseudo potential energy is a function of the mismatch and so effectively a function of the particle velocity parallel to the background magnetic field (compare to normal potential energy which is a function of position). Analysis of the pseudo-potential provides a means for interpreting particle motion in the wave in a manner analogous to the analysis of a normal particle bouncing in a conventional potential well.&#160; The wave-particle&#160; interaction is electromagnetic and so differs from and is more complicated than the well-known Landau damping of electrostatic waves.&#160; The pseudo-potential profile depends on the initial mismatch, the normalized wave amplitude, and the initial angle between the wave magnetic field and the particle perpendicular velocity. For zero initial mismatch, the pseudo-potential consists of only one valley, but for finite mismatch, there can be two valleys separated by a hill. A large pitch angle scattering of the energetic electron can occur in the two-valley situation but fast scattering can also occur in a single valley. Examples relevant to magnetospheric whistler waves are discussed. Extension to the situation of a distribution of relativistic particles is presented in a companion talk [2].[1] P. M. Bellan, Phys. Plasmas 20, Art. No. 042117 (2013)[2] Y. D. Yoon and P. M. Bellan, JGR 125, Art. No. e2020JA027796 (2020)

Simulation of the Scattering of Continuously Injected Pickup Ions outside the Heliopause

The Astrophysical Journal ◽

10.3847/1538-4357/ac2a2e ◽

2021 ◽

Vol 922 (2) ◽

pp. 271

Author(s):

Ding Sheng ◽

Kaijun Liu ◽

V. Florinski ◽

J. D. Perez

Keyword(s):

Magnetic Field ◽

Pitch Angle ◽

Injection Rate ◽

Angle Distribution ◽

Pickup Ions ◽

Isotropic Distribution ◽

Angle Scattering ◽

First Time ◽

Continuous Injection

Abstract Hybrid simulations in 2D space and 3D velocity dimensions with continuous injection of pickup ions (PUIs) provide insight into the plasma processes that are responsible for the pitch angle scattering of PUIs outside the heliopause. The present investigation includes for the first time continuous injection of PUIs and shows how the scattering depends on the energy of the PUIs and the strength of the background magnetic field as well as the dependence on the injection rate of the time for the isotropization of the pitch angle distribution. The results demonstrate that, with the gradual injection of PUIs of a narrow ring velocity distribution perpendicular to the background magnetic field, oblique mirror mode waves develop first, followed by the growth of quasiparallel propagating ion cyclotron waves. Subsequently, the PUIs are scattered by the excited waves and gradually approach an isotropic distribution. A time for isotropization is defined to be the time at which T ∣∣/T ⊥, i.e., the ratio of the parallel to perpendicular PUI thermal energy changes from ≈0 to ≈0.15. By varying the PUI injection rate, estimates of the time for the PUI distribution to be isotropized are presented. The isotropization time obtained is shorter, ≈ months, than the time, ≈ years, required by the conventional secondary ENA mechanism to explain the IBEX ENA ribbon.

Non-diffusive pitch-angle scattering of a distribution of energetic particles by coherent whistler waves

10.5194/egusphere-egu21-3604 ◽

2021 ◽

Author(s):

Young Dae Yoon ◽

Paul Bellan

Keyword(s):

Magnetic Field ◽

Single Particle ◽

Pitch Angle ◽

Present Theory ◽

Space Physics ◽

Particle Analysis ◽

Angle Scattering ◽

Particle Simulations ◽

Uniform Background

A recent study and a companion talk [1] showed that an exact rearrangement of the relativistic particle equation of motion under a coherent circularly-polarized electromagnetic wave leads to an equation describing the motion of the &#8220;frequency mismatch&#8221; parameter &#958; under a pseudo-potential &#968;(&#958;). When the particle undergoes a so-called &#8220;two-valley motion&#8221; in &#958;-space, it experiences large changes in &#958; and thus its pitch-angle because &#958; is a function of the particle&#8217;s velocity parallel to the background magnetic field. This single-particle analysis is extended [2] to a distribution of relativistic particles. First, the condition for two-valley motion is derived with parameters relevant to magnetospheric contexts. Single-particle simulations verify that particles which satisfy this condition indeed undergo large pitch-angle fluctuations. Second, assuming a relativistic Maxwellian particle distribution, the fraction of particles that undergo two-valley motion is analytically derived and is numerically verified by Monte-Carlo simulations. A significant fraction (1% - 5%) of the distribution undergoes two-valley motion for typical magnetospheric parameters. For sufficiently fast interactions where a uniform background magnetic field and a constant wave frequency can be assumed, the widely-used second-order trapping theory [3] is shown to be an erroneous approximation of the present theory.&#160;[1] P. M. Bellan, Phys. Plasmas, 20 (4), Art. No. 042117 (2013)[2] Y. D. Yoon and P. M. Bellan, JGR Space Physics, 125 (6), Art. No. e2020JA027796 (2020)[3] D. Nunn, Planet. and Space Sci., 22 (3), 349-378 (1974)&#160;

Pitch angle scattering of an energetic magnetized particle by a circularly polarized electromagnetic wave

Physics of Plasmas ◽

10.1063/1.4801055 ◽

2013 ◽

Vol 20 (4) ◽

pp. 042117 ◽

Cited By ~ 17

Author(s):

P. M. Bellan

Keyword(s):

Electromagnetic Wave ◽

Pitch Angle ◽

Circularly Polarized ◽

Large pitch-angle scattering by a circularly polarized electromagnetic wave

10.1109/iceaa52647.2021.9539815 ◽

2021 ◽

Author(s):

P. M. Bellan

Keyword(s):

Electromagnetic Wave ◽

Pitch Angle ◽

Circularly Polarized ◽

Low-frequency plasma waves and ion pitch angle scattering at large distances (>3.5 × 105km) from Giacobini-Zinner: Interplanetary magnetic field α dependences

Journal of Geophysical Research Atmospheres ◽

10.1029/ja094ia01p00018 ◽

1989 ◽

Vol 94 (A1) ◽

pp. 18 ◽

Cited By ~ 30

Author(s):

Bruce T. Tsurutani ◽

D. Edgar Page ◽

Edward J. Smith ◽

Bruce E. Goldstein ◽

Armando L. Brinca ◽

...

Keyword(s):

Magnetic Field ◽

Interplanetary Magnetic Field ◽

Pitch Angle ◽

Low Frequency ◽

Plasma Waves ◽

Angle Scattering ◽

Frequency Plasma

First in situ evidence of electron pitch angle scattering due to magnetic field line curvature in the Ion diffusion region

Journal of Geophysical Research Space Physics ◽

10.1002/2016ja022409 ◽

2016 ◽

Vol 121 (5) ◽

pp. 4103-4110 ◽

Cited By ~ 5

Author(s):

Y. C. Zhang ◽

C. Shen ◽

A. Marchaudon ◽

Z. J. Rong ◽

B. Lavraud ◽

...

Keyword(s):

Magnetic Field ◽

Field Line ◽

Magnetic Field Line ◽

Pitch Angle ◽

Diffusion Region ◽

Ion Diffusion ◽

Magnetic Field Amplification and Polar Jet Formation in Protostars

Symposium - International Astronomical Union ◽

10.1017/s0074180900096017 ◽

1987 ◽

Vol 115 ◽

pp. 384-384

Author(s):

S. Hinata

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Kinetic Energy ◽

Accretion Disk ◽

Outer Edge ◽

Moment Of Inertia ◽

Simple Relationship ◽

Field Amplification ◽

The Moment

There is a simple relationship among moment of inertia I, rotational kinetic energy K, and momentum L given by (David Layzer, private communication), 2IK ≧ L. During the Hayashi phase a rotating protostar will amplify the trapped magnetic field by a dynamo-like process. Since the rotation is expected to be fast, many unstable modes will be excited and will grow exponentially in time until some nonlinear processes saturate the amplitude. However, it may happen that the reduction in rotational kinetic energy becomes so large that without increasing the moment of inertia the inequality given above may not be satisfied. The only way to increase the moment of inertia is to move the mass outward. This can be done by transferring the angular momentum outward through the magnetic field. So we will have a fast rotating mass shell at the outer edge of the star. Further transfer of angular momentum will push the shell against the accretion disk; the moving masses of the disk will divert the mass flow along the background magnetic field which extends perpendicular to the accretion disk. This results in the hollow cone jets from both poles because the outward motion is primarily on the equatorial plane.

Relativistic electron dropouts by pitch angle scattering in the geomagnetic tail

Annales Geophysicae ◽

10.5194/angeo-24-3151-2006 ◽

2006 ◽

Vol 24 (11) ◽

pp. 3151-3159 ◽

Cited By ~ 9

Author(s):

J. J. Lee ◽

G. K. Parks ◽

K. W. Min ◽

M. P. McCarthy ◽

E. S. Lee ◽

...

Keyword(s):

Magnetic Field ◽

Relativistic Electron ◽

Magnetic Moment ◽

Pitch Angle ◽

Electron Flux ◽

Electron Precipitation ◽

Precipitation Event ◽

Real Field ◽

Geomagnetic Tail ◽

Abstract. Relativistic electron dropout (RED) events are characterized by fast electron flux decrease at the geostationary orbit. It is known that the main loss process is non adiabatic and more effective for the high energy particles. RED events generally start to occur at midnight sector and propagate to noon sector and are correlated with magnetic field stretching. In this paper, we discuss this kind of event can be caused from pitch angle diffusion induced when the gyro radius of the electrons is comparable to the radius of curvature of the magnetic field and the magnetic moment is not conserved any more. While this process has been studied theoretically, the question is whether electron precipitation could be explained with this process for the real field configuration. This paper will show that this process can successfully explain the precipitation that occurred on 14 June 2004 observed by the low-altitude (680 km) polar orbiting Korean satellite, STSAT-1. In this precipitation event, the energy dispersion showed higher energy electron precipitation occurred at lower L values. This feature is a good indicator that precipitation was caused by the magnetic moment scattering in the geomagnetic tail. This interpretation is supported by the geosynchronous satellite GOES observations that showed significant magnetic field distortion occurred on the night side accompanying the electron flux depletion. Tsyganenko-01 model also shows the magnetic moment scattering could occur under the geomagnetic conditions existing at that time. We suggest the pitch angle scattering by field curvature violating the first adiabatic invariant as a possible candidate for loss mechanism of relativistic electrons in radiation belt.

Theory of Raman sidescatter from a magnetized plasma

Journal of Plasma Physics ◽

10.1017/s0022377800002087 ◽

1984 ◽

Vol 32 (2) ◽

pp. 331-346 ◽

Cited By ~ 1

Author(s):

H. C. Barr ◽

T. J. M. Boyd ◽

R. Rankin

Keyword(s):

Magnetic Field ◽

Electromagnetic Wave ◽

Growth Rates ◽

Scattered Light ◽

Critical Density ◽

Magnetized Plasma ◽

Frequency Shifts ◽

Wave Growth ◽

Circularly Polarized ◽

The Magnetic Field

The effects of a d.c. magnetic field on stimulated Raman sidescatter from laser-produced plasmas is studied. For exact sidescatter along the magnetic field, the Raman instability separates into two distinct decays in which the scattered light is either a right (RHCP) or left (LHCP) circularly polarized electromagnetic wave. Growth rates of the instabilities can be enhanced in the former case but are diminished in the latter. The magnetic field induced effects are greatest near the quarter critical density where frequency shifts can be especially significant, being equal to ± ¼Ωc for decay into RHCP and LHCP waves, respectively.