Results

Introduction

Presented here are some main results for which the QShock code has been used. (not a complete list, see publications for better view)

Particle acceleration by multiple parallel shocks

Numerical simulations and semi-analytical results on acceleration of electrons in multiple parallel shocks. We study acceleration by a weak(ish) internal shock propagating into the downstream of a strong external shock. Preliminary results were published in the "30th International Cosmic Ray Conference". ... more

Related publications:
- Tammi J. & Dempsey P. 2007, Proc. ICRC 2007

Particle acceleration in thick parallel shock with large compression

We report studies on first-order Fermi acceleration in parallel modified shock waves with a large scattering center compression ratio expected from turbulence transmission models. Using a Monte Carlo technique we have modeled particle acceleration in shocks with a velocity ranging from nonrelativistic to ultrarelativistic and a thickness extending from nearly steplike to very wide structures exceeding the particle diffusion length by orders of magnitude. The nonrelativistic diffusion approximation is found to be surprisingly accurate in predicting the spectral index of a thick shock with large compression ratio even in the cases involving relativistic shock speeds. ... more

Related publications:
- Virtanen J.J.P., Vainio R. 2005, A&A 439, 461
- Vainio R., Virtanen J.J.P. & Schlickeiser R. 2003, A&A 409, 821
- Vainio R., Virtanen J.J.P. & Schlickeiser R. 2005, A&A 431, 7

Second-order Fermi acceleration in parallel relativistic shocks

We present results of test-particle simulations on both the first and the second order Fermi acceleration (i.e. stochastic acceleration) for relativistic parallel shock waves. Our simulations cover cases of particles injected and accelerated first at the shock and then continued accelerating in the stochastic process in the downstream region, and particles that are accelerated in the downstream. We show that depending on the magnetic field strength and turbulence the stochastic mechanism can have considerable effects on very short temporal and spatial scales. Our findings suggest that the role of the second order mechanism in the turbulent downstream of a relativistic shock with respect to the first order mechanism at the shock front may have been underestimated in the past, and that the second order mechanism may have significant effects on the form of the particle spectra and its time evolution. ... more

Related publications:
- Virtanen J.J.P., Vainio R. 2005, ApJ 621, 313
- Vainio R., Virtanen J.J.P. & Schlickeiser R. 2003, A&A 409, 821
- Vainio R., Virtanen J.J.P. & Schlickeiser R. 2005, A&A 431, 7

Effects of the injection method and the form of the flow profile to the acceleration efficiency

We have used Monte Carlo simulations to study the properties of particle acceleration in relativistic shocks that have a non-trivial structure:a finite width and a special velocity profile. The numerical modeling indicates that (i) rigidity dependence of the mean free path and (ii) the electron injection energy crucially affect the shape of the electron spectrum. For an energy independent mean free path, a spectral index of 3.2 of accelerated electrons is obtained for ultra-relativistic shocks with thickness determined by ion dynamics. The value of 2.2 previously computed by several authors for a step-like shock is obtained as a high-energy limit for a mean free path increasing as a function of energy.

Related publications:
- Virtanen J.J.P., Vainio R. 2003, in ''The 28:th International Cosmic Ray Conference'', Tsukuba, Japan, August 2003, OG 1.4, 2023
- Vainio R., Virtanen J.J.P. in ''Particle Acceleration in Astrophysical Objects'' conference, Cracow, Poland, June 2003; electronic proceedings

Effect of the thickness of the shock front to the efficiency of the first-order Fermi acceleration

We have studied the effect of internal structure of shock fronts on their efficiency of particle acceleration. We present a simple model of the width of a parallel shock front depending on the spectral index of the ambient magnetic turbulence. Using Monte-Carlo simulations, we determine the spectral index of energy distribution of shock accelerated particles in this model as well as in a case, where the shock width is independent of the ambient turbulence. In both cases, the acceleration capability of a wide shock structure is shown to be much smaller than for a step-like shock front.

Related publications:
- Virtanen J.J.P., Vainio R. 2003, in ''High Energy Blazar Astronomy'' workshop, Tuorla, Finland, June 2002, eds. L.O. Takalo, E. Valtaoja, ASP Conf. Proc. Vol. 299, 157