The possibility that charged particles are accelerated statistically in a “sea” of small-scale interacting magnetic flux
ropes in the supersonic solar wind is gaining credence. In this Letter, we extend the Zank et al. statistical transport
theory for a nearly isotopic particle distribution by including an escape term corresponding to particle loss from a
finite acceleration region. Steady-state 1D solutions for both the accelerated particle velocity distribution function
and differential intensity are derived. We show Ulysses observations of an energetic particle flux enhancement
event downstream of a shock near 5 au that is inconsistent with the predictions of classical diffusive shock
acceleration (DSA) but may be explained by local acceleration associated with magnetic islands. An automated
Grad-Shafranov reconstruction approach is employed to identify small-scale magnetic flux ropes behind the shock.
For the first time, the observed energetic particle “time-intensity” profile and spectra are quantitatively compared
with theoretical predictions. The results show that stochastic acceleration by interacting magnetic islands accounts
successfully for the observed (i) peaking of particle intensities behind the shock instead of at the shock front
as standard DSA predicts; (ii) increase in the particle flux amplification factor with increasing particle energy;
(ii) increase in distance between the particle intensity peak and the shock front with increasing energy; and
(iv) hardening of particle power-law spectra with increasing distance downstream of the shock.
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Interaction between Multiple Current Sheets and a Shock Wave: 2D Hybrid Kinetic Simulations
Abstract Particle acceleration behind a shock wave due to interactions between magnetic islands in the heliosphere has attracted attention in recent years. The downstream acceleration may yield a continuous increase of particle flux downstream of the shock wave. Although it is not obvious how the downstream magnetic islands are produced, it has been suggested that current sheets are involved in the generation of magnetic islands due to their interaction with a shock wave. We perform 2D hybrid kinetic simulations to investigate the interaction between multiple current sheets and a shock wave. In the simulation, current sheets are compressed by the shock wave and a tearing instability develops at the compressed current sheets downstream of the shock. As the result of this instability, the electromagnetic fields become turbulent and magnetic islands form well downstream of the shock wave. We find a “post-cursor” region in which the downstream flow speed normal to the shock wave in the downstream rest frame is decelerated to ∼ 1 V A immediately behind the shock wave, where V A is the upstream Alfvén speed. The flow speed then gradually decelerates to 0 accompanied by the development of the tearing instability. We also observe an efficient production of energetic particles above 100 E 0 during the development of the instability some distance downstream of the shock wave, where E 0 = m p V A 2 and m p is the proton mass. This feature corresponds to Voyager observations showing that the anomalous cosmic-ray intensity increase begins some distance downstream of the heliospheric termination shock.
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- Award ID(s):
- 1655280
- NSF-PAR ID:
- 10308614
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 922
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The possibility that charged particles are accelerated statistically in a “sea” of small-scale interacting magnetic flux ropes in the supersonic solar wind is gaining credence. In this Letter, we extend the Zank et al. statistical transport theory for a nearly isotopic particle distribution by including an escape term corresponding to particle loss from a finite acceleration region. Steady-state 1D solutions for both the accelerated particle velocity distribution function and differential intensity are derived. We show Ulysses observations of an energetic particle flux enhancement event downstream of a shock near 5 au that is inconsistent with the predictions of classical diffusive shock acceleration (DSA) but may be explained by local acceleration associated with magnetic islands. An automated Grad-Shafranov reconstruction approach is employed to identify small-scale magnetic flux ropes behind the shock. For the first time, the observed energetic particle “time-intensity” profile and spectra are quantitatively compared with theoretical predictions. The results show that stochastic acceleration by interacting magnetic islands accounts successfully for the observed (i) peaking of particle intensities behind the shock instead of at the shock front as standard DSA predicts; (ii) increase in the particle flux amplification factor with increasing particle energy; (ii) increase in distance between the particle intensity peak and the shock front with increasing energy; and (iv) hardening of particle power-law spectra with increasing distance downstream of the shock.more » « less
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Abstract We investigate the interaction of turbulence with shock waves by performing 2D hybrid kinetic simulations. We inject force-free magnetic fields upstream that are unstable to the tearing-mode instability. The magnetic fields evolve into turbulence and interact with a shock wave whose sonic Mach number is 2.4. Turbulence properties, the total and normalized residual energy and the normalized cross helicity, change across the shock wave. While the energy of velocity and magnetic fluctuations is mostly distributed equally upstream, the velocity fluctuations are amplified dominantly downstream of the shock wave. The amplitude of turbulence spectra for magnetic, velocity, and density fluctuations are also increased at the shock wave while their spectral index remains unchanged. We compare our results with the Zank et al. model of turbulence transmission across a shock, and find that it provides a reasonable explanation for the spectral change across the shock wave. We find that particles are efficiently accelerated at the shock front, and a power-law spectrum forms downstream. This can be explained by diffusive shock acceleration, in which particles gain energy by being scattered upstream and downstream of a shock wave. The trajectory of an accelerated particle suggests that upstream turbulence plays a role scattering of particles.more » « less
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Abstract Magnetic reconnection in a quasi‐parallel bow shock is investigated with two‐dimensional local particle‐in‐cell simulations. In the shock transition and downstream regions, large amplitude magnetic fluctuations exist, and abundant current sheets form. In some current sheets, reconnection occurs, and ion‐scale and electron‐scale magnetic islands are generated. In electron‐scale island regions, only electron outflow jets are observed, producing a quadrupolar out‐of‐plane magnetic field pattern, while in ion‐scale islands, both ions and electrons are involved and energized in reconnection. Normalized reconnection rates are obtained to be between around 0.1 to 0.2, and particle acceleration signatures are seen in distribution functions.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3847/1538-4357/ac2e06
