Proton Larmor Radius Research Articles

Conditions for arrival of solar energetic protons in Earth after strong solar flares

We analyze the Sun-to-Earth transport of energetic protons accelerated in solar flares. We use a model which assumes that protons move earthward in the Parker electromagnetic field. In this model, protons are shown to be recorded on Earth when they, moving away from the solar flare region, reach the vicinity of the heliospheric current sheet, while Earth is at a distance smaller than the proton Larmor radius from the current sheet neutral line. We present the analysis of experimental data on solar flares in August–September 2011. This analysis shows that the absence of energetic protons recording in the vicinity of Earth for some major solar flares can be explained by the proposed model.

Условия прихода солнечных энергичных протонов на Землю после мощных вспышек на Солнце

We analyze the Sun-to-Earth transport of energetic protons accelerated in solar flares. We use a model which assumes that protons move earthward in the Parker electromagnetic field. In this model, protons are shown to be recorded on Earth when they, moving away from the solar flare region, reach the vicinity of the heliospheric current sheet, while Earth is at a distance smaller than the proton Larmor radius from the current sheet neutral line. We present the analysis of experimental data on solar flares in August–September 2011. This analysis shows that the absence of energetic protons recording in the vicinity of Earth for some major solar flares can be explained by the proposed model.

Electron Heating by Kinetic Alfvén Waves in Coronal Loop Turbulence

Abstract A test-particle model describing the energization of electrons in a turbulent plasma is presented. Parameters are chosen to represent turbulence in a magnetic structure of the solar corona. A fluctuating electric field component parallel to the background magnetic field, with properties similar to those of Kinetic Alfvén Waves, is assumed to be present at scales of the order of the proton Larmor radius. Electrons are stochastically accelerated by multiple interactions with such fluctuations, reaching energies of the order of 102 eV within tens to hundreds of seconds, depending on the turbulence amplitude. For values of the large-scale plasma velocity fluctuation of the order of tens of kilometers per second, the power absorbed by electrons per surface unit is of the order of that typically necessary to heat the corona. The power that electrons absorb from fluctuations is proportional to the third power of the large-scale velocity amplitude, and is comparable with the power associated with the turbulent cascade. Therefore, this mechanism can be considered as an equivalent kinetic dissipation for turbulence, and it can play a relevant role in the heating of electrons in the corona.

Time Evolution of the Macroscopic Characteristics of a Thin Current Sheet in the Course of Its Formation in the Earth’s Magnetotail

A numerical model is developed that allows tracing the time evolution of a current sheet from a relatively thick current configuration with isotropic distributions of the pressure and temperature in an extremely thin current sheet, which plays a key role in geomagnetic processes. Such a configuration is observed in the Earth’s magnetotail in the stage preceding a large-scale geomagnetic disturbance (substorm). Thin current sheets are reservoirs of the free energy released during geomagnetic disturbances. The time evolution of the components of the pressure tensor caused by changes in the structure of the current sheet is investigated. It is shown that the pressure tensor in the current sheet evolves in two stages. In the first stage, a current sheet with a thickness of eight to ten proton Larmor radii forms. This stage is characterized by the plasma drift toward the current sheet and the Earth and can be described in terms of the Chu–Goldberger–Low approximation. In the second stage, an extremely thin current sheet with an anisotropic plasma pressure tensor forms, due to which the system is maintained in an equilibrium state. Estimates of the characteristic time of the system evolution agree with available experimental data.

HELIOSHEATH MAGNETIC FIELD AND PLASMA OBSERVED BY VOYAGER 2 DURING 2012 IN THE RISING PHASE OF SOLAR CYCLE 24

ABSTRACT We discuss magnetic field and plasma observations of the heliosheath made by Voyager 2 (V2) during 2012, when V2 was observing the effects of increasing solar activity following the solar minimum in 2009. The average magnetic field strength B was 0.14 nT and B reached 0.29 nT on day 249. V2 was in a unipolar region in which the magnetic polarity was directed away from the Sun along the Parker spiral 88% of the time, indicating that V2 was poleward of the heliospheric current sheet throughout most of 2012. The magnetic flux at V2 during 2012 was constant. A merged interaction region (MIR) was observed, and the flow speed increased as the MIR moved past V2. The MIR caused a decrease in the >70 MeV nuc−1 cosmic-ray intensity. The increments of B can be described by a q-Gaussian distribution with q = 1.2 ± 0.1 for daily averages and q = 1.82 ± 0.03 for hour averages. Eight isolated current sheets (“PBLs”) and four closely spaced pairs of current sheets were observed. The average change of B across the current sheets was a factor of ≈2, and B increased or decreased with equal probability. Magnetic holes and magnetic humps were also observed. The characteristic size of the PBLs was ≈6 R L, where R L is the Larmor radius of protons, and the characteristic sizes of the magnetic holes and humps were ≈38 R L and ≈11 R L, respectively.

Review on Current Sheets in CME Development: Theories and Observations

We introduce how the catastrophe model for solar eruptions predicted the formation and development of the long current sheet (CS) and how the observations were used to recognize the CS at the place where the CS is presumably located. Then, we discuss the direct measurement of the CS region thickness by studying the brightness distribution of the CS region at different wavelengths. The thickness ranges from to about at heights between 0.27 and from the solar surface. But the traditional theory indicates that the CS is as thin as the proton Larmor radius, which is of order tens of meters in the corona. We look into the huge difference in the thickness between observations and theoretical expectations. The possible impacts that affect measurements and results are studied, and physical causes leading to a thick CS region in which reconnection can still occur at a reasonably fast rate are analyzed. Studies in both theories and observations suggest that the difference between the true value and the apparent value of the CS thickness is not significant as long as the CS could be recognised in observations. We review observations that show complex structures and flows inside the CS region and present recent numerical modelling results on some aspects of these structures. Both observations and numerical experiments indicate that the downward reconnection outflows are usually slower than the upward ones in the same eruptive event. Numerical simulations show that the complex structure inside CS and its temporal behavior as a result of turbulence and the Petschek-type slow-mode shock could probably account for the thick CS and fast reconnection. But whether the CS itself is that thick still remains unknown since, for the time being, we cannot measure the electric current directly in that region. We also review the most recent laboratory experiments of reconnection driven by energetic laser beams, and discuss some important topics for future works.

Microphysics of Cosmic Plasmas: Hierarchies of Plasma Instabilities from MHD to Kinetic

In this article, we discuss the idea of a hierarchy of instabilities that can rapidly couple the disparate scales of a turbulent plasma system. First, at the largest scale of the system, L, current carrying flux ropes can undergo a kink instability. Second, a kink instability in adjacent flux ropes can rapidly bring together bundles of magnetic flux and drive reconnection, introducing a new scale of the current sheet width, l, perhaps several ion inertial lengths (δ i ) across. Finally, intense current sheets driven by reconnection electric fields can destabilize kinetic waves such as ion cyclotron waves as long as the drift speed of the electrons is large compared to the ion thermal speed, v D ≫v i . Instabilities such as these can couple MHD scales to kinetic scales, as small as the proton Larmor radius, ρ i .

Fermi Acceleration in Plasmoids Interacting with Fast Shocks of Reconnection via Fractal Reconnection

We propose the particle acceleration model coupled with multiple plasmoid ejections in a solar flare. Unsteady reconnection produces plasmoids in a current sheet and ejects them out to the fast shocks, where particles in a plasmoid are reflected upstream the shock front by magnetic mirror effect. As the plasmoid passes through the shock front, the reflection distance becomes shorter and shorter driving Fermi acceleration, until it becomes proton Larmor radius. The fractal distribution of plasmoids may also have a role in naturally explaining the power-law spectrum in nonthermal emissions.

Detection of Small-Scale Structures in the Dissipation Regime of Solar-Wind Turbulence

Recent observations of the solar wind have pointed out the existence of a cascade of magnetic energy from the scale of the proton Larmor radius ρ(p) down to the electron Larmor radius ρ(e) scale. In this Letter we study the spatial properties of magnetic field fluctuations in the solar wind and find that at small scales the magnetic field does not resemble a sea of homogeneous fluctuations, but rather a two-dimensional plane containing thin current sheets and discontinuities with spatial sizes ranging from l >/~ ρ(p) down to ρ(e) and below. These isolated structures may be manifestations of intermittency that localize sites of turbulent dissipation. Studying the relationship between turbulent dissipation, reconnection, and intermittency is crucial for understanding the dynamics of laboratory and astrophysical plasmas.

Cluster and TC-1 observation of magnetic holes in the plasma sheet

Abstract. Magnetic holes with relatively small scale sizes, detected by Cluster and TC-1 in the magnetotail plasma sheet, are studied in this paper. It is found that these magnetic holes are spatial structures and they are not magnetic depressions generated by the flapping movement of the magnetotail current sheet. Most of the magnetic holes (93%) were observed during intervals with Bz larger than Bx, i.e. they are more likely to occur in a dipolarized magnetic field topology. Our results also suggest that the occurrence of these magnetic holes might have a close relationship with the dipolarization process. The magnetic holes typically have a scale size comparable to the local proton Larmor radius and are accompanied by an electron energy flux enhancement at a 90° pitch angle, which is quite different from the previously observed isotropic electron distributions inside magnetic holes in the plasma sheet. It is also shown that most of the magnetic holes occur in marginally mirror-stable environments. Whether the plasma sheet magnetic holes are generated by the mirror instability related to ions or not, however, is unknown. Comparison of ratios, scale sizes and propagation direction of magnetic holes detected by Cluster and TC-1, suggests that magnetic holes observed in the vicinity of the TC-1 orbit (~7–12 RE) are likely to be further developed than those observed by Cluster (~7–18 RE).

Embedded current sheets in the Earth’s magnetotail

[1] In this investigation we introduce and discuss quantitative parameters of a thin current sheet embedded in the background plasma sheet. We use Cluster statistics and empirical models, as well as self-consistent simulations, to understand the formation and development of embedded current sheets, in particular in the course of substorms. Data and theory show that the embedded sheet thickness is of the order of a proton larmor radius, a constraint equivalent to magnetic flux conservation. The embedded sheet can be essentially described by two dimensionless parameters B0/Bext and F0/Fext. B0 is the magnetic field at the embedded sheet boundary, Bext is the field at the boundary of the background plasma sheet, and F0 and Fext are magnetic flux values. During the growth phase current density in embedded sheet and B0 increase, while thickness decreases. Sheets with the most intense currents (large B0) are observed after onset. The self-consistent anisotropic sheet model, including both electron and proton currents and combined with the Harris-type background shows that when the proton-scale embedded sheet becomes sufficiently thin, an electron-scale current sheet can appear inside it due to enhanced electron curvature drift.

THE HEATING OF TEST PARTICLES IN NUMERICAL SIMULATIONS OF ALFVÉNIC TURBULENCE

We study the heating of charged test particles in three-dimensional numerical simulations of weakly compressible magnetohydrodynamic (MHD) turbulence (``Alfvenic turbulence''); these results are relevant to particle heating and acceleration in the solar wind, solar flares, accretion disks onto black holes, and other astrophysics and heliospheric environments. The physics of particle heating depends on whether the gyrofrequency of a particle is comparable to the frequency of a turbulent fluctuation that is resolved on the computational domain. Particles with these frequencies nearly equal undergo strong perpendicular heating (relative to the local magnetic field) and pitch angle scattering. By contrast, particles with large gyrofrequency undergo strong parallel heating. Simulations with a finite resistivity produce additional parallel heating due to parallel electric fields in small-scale current sheets. Many of our results are consistent with linear theory predictions for the particle heating produced by the Alfven and slow magnetosonic waves that make up Alfvenic turbulence. However, in contrast to linear theory predictions, energy exchange is not dominated by discrete resonances between particles and waves; instead, the resonances are substantially ``broadened.'' We discuss the implications of our results for solar and astrophysics problems, in particular the thermodynamics of the near-Earth solar wind. We conclude that Alfvenic turbulence produces significant parallel heating via the interaction between particles and magnetic field compressions (``slow waves''). However, on scales above the proton Larmor radius, Alfvenic turbulence does not produce significant perpendicular heating of protons or minor ions.

The Sun as a MHD generator: application of a new heating mechanism for the coronal loops and closed magnetic structures

We investigate a possibility of heating of the loops and other closed magnetic structures in active regions of the solar corona by the flow of solar wind (plus other flows that may be present) across the magnetic field lines (that are perpendicular to the flow), in a similar manner as a conventional MHD generator works. A simple model is formulated which allows to calculate the typical currents generated by this mechanism. This enables to make a judgement whether the loops in solar active regions can be heated by the proposed mechanism through the associated Ohmic dissipation. It is shown that even if the heating region width is of the order of a few proton Larmor radii (this effectively means that a loop is represented by {\it nano-threads}, by analogy with the nano-flare coronal heating mechanism, with width of a few proton Larmor radii) and the plasma flow speed is 50 km s$^{-1}$ then only about 1% of the heating requirement of coronal loops could be met under this conjecture. Other implications of the model, such as a predicted spatial heat distribution along the loop as well as application of the model to the other places e.g. chromosphere and corotating interaction region structures in the solar wind are discussed.

The Magnetorotational Instability in a Collisionless Plasma

We consider the linear axisymmetric stability of a differentially rotating collisionless plasma in the presence of a weak magnetic field; we restrict our analysis to wavelengths much larger than the proton Larmor radius. This is the kinetic version of the magnetorotational instability explored extensively as a mechanism for magnetic field amplification and angular momentum transport in accretion disks. The kinetic calculation is appropriate for hot accretion flows onto compact objects and for the growth of very weak magnetic fields, where the collisional mean free path is larger than the wavelength of the unstable modes. We show that the kinetic instability criterion is the same as in MHD, namely that the angular velocity decrease outward. However, nearly every mode has a linear kinetic growth rate that differs from its MHD counterpart. The kinetic growth rates also depend explicitly on β, i.e., on the ratio of the gas pressure to the pressure of the seed magnetic field. For β ~ 1 the kinetic growth rates are similar to the MHD growth rates, while for β 1 they differ significantly. For β 1, the fastest growing mode has a growth rate ≈ Ω for a Keplerian disk, larger than its MHD counterpart; there are also many modes whose growth rates are negligible, β-1/2Ω Ω. We provide a detailed physical interpretation of these results and show that gas pressure forces, rather than just magnetic forces, are central to the behavior of the magnetorotational instability in a collisionless plasma. We also discuss the astrophysical implications of our analysis.

Three‐dimensional hybrid simulation of solar wind interaction with unmagnetized planets

The interaction between the solar wind and unmagnetized planets was investigated using computer simulation and a three‐dimensional hybrid code that treats kinetic ions and massless fluid electrons. In the simulation the planet was treated as an ionized gaseous body with uniform and constant supply of plasma. The results given in this paper showed that the shock size and magnetic barrier intensity are asymmetrical in the direction of the convection electric field because of oxygen ions escaping from the side of the planet to which the electric field was pointing. The calculated asymmetry in the magnetic barrier intensity was consistent with observations, although the direction of the calculated asymmetry in the shock size did not match the asymmetry observed near either Venus or Mars. When the planet size was comparable to the Larmor radius of protons, a multiple‐shock structure was observed in the simulation. It is suggested that this structure is due to dispersion of the magnetosonic waves caused by the finite Larmor radius of protons. The simulation results also showed that ions escaped to the magnetotail through the tail rays and that the tail rays were connected with the plasma sheet.

Three-dimensional hybrid simulation of magnetized plasma flow around an obstacle

The interaction between the magnetized plasma flow and an obstacle was investigated in the computer simulations described here by using a three-dimensional hybrid code (kinetic ions and massless fluid electrons). The results, which are relevant to the interaction between the solar wind and an unmagnetized planet (Venus or Mars), show that fundamental structures (bow shock and magnetotail) are formed. When a reflecting boundary is used at the obstacle, the magnetic field configuration was clearly asymmetrical in the direction of the convection electric field. This asymmetry is a result of differences in ion acceleration due to the convection electric field. Asymmetry is also evident when the size of the obstacle is close to the Larmor radius of protons. The shock of a smaller obstacle is weaker than that of a larger obstacle, but the shock size is almost independent of the obstacle size.

Crossed E×B-Fields Back-Bombardment Instability and Ion Cyclotron Heating of Gas-Discharge Plasma Streams

The article present our recent results of computer simulations and theory analysis concerning of dynamics of the crossed E×B-fields back-bombardment (BKB) instability in magnetron diodes. The concept of the BKB-instability applied to show new explanation for known experimental data of an intense ion heating in accelerated plasma streams. Main features of the BKB-instability into ion diodes are following: 1) ion magnetic insulation is d0 > ri where d0 is accelerating gap across applied magnetic field B0, ri = 5V00.5/B0 is proton Larmor radius, cm; V0 – applied voltage, kV; B0 – kG; 2) EA ≠ 0 is high electric field on self or secondary emission anode electrodes; 3) main frequency oscillation of fs = fci/2 = 0.76 B0 MHz; 4) convert power efficiency of ηB = P~/P0 is up to 50%.Radial proton HF-oscillations current density of the Jir provided by the BKB-instability excites magnetohydrodynamics waves. They are propagated in the tube plasma with azimuthal velocity v∼9 ~ 107 cm/s (Miv∼92 ~ eV0) and along the B0 with the vA ~ 4×107 cm/s -Alfven velocity. Known experimental data was demonstrated a level of the HF-oscillation power which was absorbed by proton streams by ion cyclotron heating equals up to 30% total supply power of the 1 MW.Work supported by RFFI under grant 96-02-19215.

Particle Heating by Alfvenic Turbulence in Hot Accretion Flows

Recent work on Alfvenic turbulence by Goldreich & Sridhar (1995; GS) suggests that the energy cascades almost entirely perpendicular to the local magnetic field. As a result, the cyclotron resonance is unimportant in dissipating the turbulent energy. Motivated by the GS cascade, we calculate the linear collisionless dissipation of Alfven waves with frequencies much less than the proton cyclotron frequency, but with perpendicular wavelengths of order the Larmor radius of thermal protons. In plasmas appropriate to hot accretion flows (proton temperature much greater than electron temperature) the dissipated Alfven wave energy primarily heats the protons. For a plasma with $\beta \lsim 5$, however, where $\beta$ is the ratio of the gas pressure to the magnetic pressure, the MHD assumptions utilized in the GS analysis break down before most of the energy in Alfven waves is dissipated; how the cascade then proceeds is unclear. Hot accretion flows, such as advection dominated accretion flows (ADAFs), are expected to contain significant levels of MHD turbulence. This work suggests that, for $\beta \gsim 5$, the Alfvenic component of such turbulence primarily heats the protons. Significant proton heating is required for the viability of ADAF models. We contrast our results on particle heating in ADAFs with recent work by Bisnovatyi-Kogan & Lovelace (1997).

Pickup protons and pressure‐balanced structures: Voyager 2 observations in merged interaction regions near 35 AU

Five pressure‐balanced structures, each with a scale of the order of a few hundredths of an astronomical unit (AU), were identified in two merged interaction regions (MIRs) near 35 AU in the Voyager 2 plasma and magnetic field data. They include a tangential discontinuity, simple and complex magnetic holes, slow correlated variations among the plasma and magnetic field parameters, and complex uncorrelated variations among the parameters. The changes in the magnetic pressure in these events are balanced by changes in the pressure of interstellar pickup protons. Thus the pickup protons probably play a major role in the dynamics of the MIRs. The solar wind proton and electron pressures are relatively unimportant in the MIRs at 35 AU and beyond. The region near 35 AU is a transition region: the Sun is the source of the magnetic field, but the interstellar medium is the source of pickup protons. Relative to the solar wind proton gyroradius, the thicknesses of the discontinuities and simple magnetic holes observed near 35 AU are at least an order of magnitude greater than those observed at 1 AU. However, the thicknesses of the tangential discontinuity and simple magnetic holes observed near 35 AU (in units of the pickup proton Larmor radius) are comparable to those observed at 1 AU (in units of the solar wind proton gyroradius). Thus the gyroradius of interstellar pickup protons controls the thickness of current sheets near 35 AU. We determine the interstellar pickup proton pressure in the PBSs. Using a model for the pickup proton temperature, we estimate that the average interstellar pickup proton pressure, temperature, and density in the MIRs at 35 AU are (0.53 ± 0.14) × 10−12 erg/cm³, (5.8 ± 0.4) × 106 °K and (7 ± 2) × 10−4 cm−3, respectively.

Upstream structure of collisionless perpendicular shocks

A full set of Vlasov–Maxwell equations describing a stationary perpendicular collisionless shock has been solved in the asymptotic case x→±∞, where x is the spatial coordinate of the one dimensional (1-D) shock geometry. The perpendicular magnetic field in the upstream region has been found to vary asymptotically as Bz(x)−Bz(−∞)∼exp(−bx/Rp), where b(MA,βp,βe)<0 is a function of the Alfvén Mach number, MA, and the proton and electron betas; Rp is the proton Larmor radius. The electron and proton distribution functions are expressed as one-dimensional integrals to be evaluated numerically. Two general results are derived: (i) there occurs an instability, in the sense that the distribution functions are not unique, for −b/MA=(mp/me)1/2, where mp and me are the proton and the electron mass, respectively. Numerical computations show that the lowest value of MA fulfilling this instability condition is Mc≊6.5. (ii) The perpendicular shock cannot develop if MA≤(1+βp+βe)1/2. Moreover, it was found that for MA, βp, and βe from a certain range, the proton distribution function exhibits a peak of reflected particles, with vx≊0 and vy≊2.33v0, i.e., with an energy of about 5.4 times that of the incident flux.