Homework from Lecture 4.

Written report topic (WRT) # 1. Assume stochastic acceleration at the loop top with a power-law spectrum of magnetic turbulence. Calculate the DSR spectrum from electrons with different non-relativistic energies.
 

WRT # 2. Assume a power-law spectrum for Langmuir wave ensemble and some number (Ax1033) of relativistic electrons with the Lorenz factor 10. Calculate the DRL spectrum.
 

WRT # 3. Calculate synchrotron emission from warm and hot components of the interstellar medium. Calculate and plot these contribution together for different filling factors.
 

WRT # 4. Assume sinusoidal oscillations of the transverse magnetic field component. Calculate modulation amplitude (or power), phase, and degree of polarization as a function of frequency.
 

WRT # 5. Assume that the particle trapping at the Masuda source is provided by scattering of the electrons by magnetic inhomogeneities with a power-law spectrum. Calculate the DSR produced by the electrons generating the above-the-loop-top hard X-ray emission (i.e., take the electron spectrum from the corresponding papers).

WRT # 6. Assume that the SNR shock wave has spherical shape, the magnetic field  downstream is amplified compared with the upstream value. Considering the change of the line of sight size (like in Eq. (5) from Berezhko et al. A&A 412, L11–L14 (2003)), calculate the radial distribution of Synchrotron X-ray brightness. For the electron distribution function take the solution from Zirakashvili and Aharonian A&A 465, 695–702 (2007). Take into account exponential decrease of the electron distribution function as in Fig. 1 Zirakashvili and Aharonian (2007).
 

For all WRT: outline the introduction for the written report. Use Latex, e.g., ApJ style (preferable).