1 / 8

Particle Acceleration

0. The observation of high-energy g -rays from space implies that particles must be accelerated to very high energies (up to ~ 10 20 eV to explain highest-energy cosmic rays). Particle Acceleration.

hamlin
Download Presentation

Particle Acceleration

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 0 The observation of high-energy g-rays from space implies that particles must be accelerated to very high energies (up to ~ 1020 eV to explain highest-energy cosmic rays). Particle Acceleration Power-law spectra observed in many objects indicate that acceleration mechanisms produce power-law particle spectra, N(g) ~ g-p Generally, d(gmv) = e (E + v x B) No strong, static electric fields (most of the regular matter in the Universe is completely ionized) => Acceleration may be related to induced electric fields (time-varying or moving magnetic fields)

  2. 0 General Idea: Particles bouncing back and forth across shock front: Particle Acceleration at Strong Shocks Shock rest frame Stationary frame of ISM v1r1 = v2r2 U v2 = (1/4)v1 v1 = U r1 / r2 = 1/4 p2, r2 p1, r1 Rest frame of shocked material v1‘ = (3/4) U v2 ‘ = (3/4)U At each pair of shock crossings, particles gain energy <DE / E> = (4/3) V/c = U/c Write E = b E0 = (1 + U/c) E0 ; b = 1 + U/c

  3. 0 Stationary frame of ISM Shock rest frame Particle Acceleration at Strong Shocks (cont.) U v1r1 = v2r2 v2 = (1/4)v1 v1 = U p2, r2 r1 / r2 = 1/4 p1, r1 Rest frame of shocked material v1‘ = (3/4) U v2 ‘ = (3/4)U Flux of particles crossing the shock front in either direction: Fcross = ¼ Nc Downstream, particles are swept away from the front at a rate : NV = ¼ NU Probability of particle to remain in the acceleration region: P = 1 - (¼ NU)/(¼ Nc) = 1 – (U/c)

  4. 0 Energy of a particle after k crossings: E = bk E0 Particle Acceleration at Strong Shocks (cont.) Number of particles remaining: N = Pk N0 => ln (N[>E]/N0) / ln (E/E0) = lnP / lnb = -1 or N(>E)/N0 = (E/E0)lnP/lnb => N(E)/N0 = (E/E0)-2

  5. 0 Weak nonrelativistic shocks p > 2 More General Cases Relativistic parallel shocks: p = 2.2 – 2.3 B U U Relativistic oblique shocks: p > 2.3 B U U

  6. 0 Effects of Cooling and Escape Evolution of particle spectra is governed by the Continuity Equation: ∂ne (g,t) . ______ ∂ __ ne (g,t) ______ = - (g ne) + Qe (g,t) - ∂t ∂g tesc,e Particle injection (acceleration on very short time scales) Escape Radiative and adiabatic losses

  7. 0 Effects of Cooling and Escape (cont.) Assume rapid particle acceleration: Q(g, t) = Q0g-q g1 < g < g2 Fast Cooling : tcool << tdyn, tesc for all particles Synchrotron or Compton spectrum: Particle spectrum: n-1/2 g-2 F(n) N(g) n-q/2 g-(q+1) n g n1 g1

  8. 0 Effects of Cooling and Escape (cont.) Assume rapid particle acceleration: Q(g, t) = Q0g-q g1 < g < g2 Slow Cooling : tcool << tdyn, tesc only for particles with g > gb Synchrotron or Compton spectrum: Particle spectrum: n-(q-1)/2 g-q F(n) N(g) n-q/2 g-(q+1) n g n1 nb g1 gb

More Related