# SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS

## Abstract

We use kinetic hybrid simulations (kinetic ions-fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.

- Authors:

- Department of Astrophysical Sciences, Princeton University, 4 Ivy Ln., Princeton, NJ 08544 (United States)

- Publication Date:

- OSTI Identifier:
- 22364694

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Astrophysical Journal Letters; Journal Volume: 798; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ACCELERATION; ASTROPHYSICS; COMPUTERIZED SIMULATION; COSMIC ELECTRONS; COSMIC RADIATION; COSMIC RAY PROPAGATION; INCLINATION; ION COLLISIONS; IONS; MAGNETIC FIELDS; PERIODICITY; REFLECTION; RELATIVISTIC RANGE; SHOCK WAVES

### Citation Formats

```
Caprioli, Damiano, Pop, Ana-Roxana, and Spitkovsky, Anatoly, E-mail: caprioli@astro.princeton.edu.
```*SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS*. United States: N. p., 2015.
Web. doi:10.1088/2041-8205/798/2/L28.

```
Caprioli, Damiano, Pop, Ana-Roxana, & Spitkovsky, Anatoly, E-mail: caprioli@astro.princeton.edu.
```*SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS*. United States. doi:10.1088/2041-8205/798/2/L28.

```
Caprioli, Damiano, Pop, Ana-Roxana, and Spitkovsky, Anatoly, E-mail: caprioli@astro.princeton.edu. Sat .
"SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS". United States.
doi:10.1088/2041-8205/798/2/L28.
```

```
@article{osti_22364694,
```

title = {SIMULATIONS AND THEORY OF ION INJECTION AT NON-RELATIVISTIC COLLISIONLESS SHOCKS},

author = {Caprioli, Damiano and Pop, Ana-Roxana and Spitkovsky, Anatoly, E-mail: caprioli@astro.princeton.edu},

abstractNote = {We use kinetic hybrid simulations (kinetic ions-fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also, by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for ion injection at non-relativistic astrophysical shocks with arbitrary strengths and magnetic inclinations, and represents a crucial ingredient for understanding the diffusive shock acceleration of cosmic rays.},

doi = {10.1088/2041-8205/798/2/L28},

journal = {Astrophysical Journal Letters},

number = 2,

volume = 798,

place = {United States},

year = {Sat Jan 10 00:00:00 EST 2015},

month = {Sat Jan 10 00:00:00 EST 2015}

}