Chapter 3: Synchrotron Radiation

Question 1

What is synchrotron radiation?

Answer 1

Radiation emitted when an electron gyrates around a magnetic field line

Question 2

What is the relativistic and non-relativistic gyrofrequency?

Answer 2

The frequency at which the velocity of synchrotron radiation perpendicular to the magnetic field undergoes circular motion.

w_B = eB/(gamma*m_0)

w_g = eB/m_e

Question 3

What is the magnetic energy density?

Answer 3

U_B = (B^2)/2mu_0

Question 4

Describe the energy loss rate and what it means for certain particles.

Answer 4

<dE/dt> = -(E^2)(e^4)(B^2)/9(pi)(epsilon_0)(c^5)(m_0)^4

Proportional to E^2 therefore high energy particles lose energy faster

Proportional to (m_0)^-4 so at given energy, electrons are most radiative

Question 5

Why does an observer only observe radiation for a small part of the particle’s orbit?

Answer 5

Due to the beaming of radiation from relativistic particles

Question 6

By what factor is the radiation in a synchrotron higher than expected and why?

Answer 6

Gamma squared due to the combo of the beaming effect and the light travel time effect

Question 7

Below a critical frequency, how can the synchrotron spectrum be described?

Answer 7

A power law of nu^1/3

Question 8

What assumptions do we make to get the spectrum from an ensemble of electrons?

Answer 8

Assume all radiation comes out at peak frequency, and ignore the theta dependence ie sin(theta)=1

Question 9

Describe the polarisation of cyclotron radiation.

Answer 9

Direction of electric field vector rotates as electron moves around its orbit, looking parallel to B field, circular polarisation. Looking perpendicular to B field, E field performs SHM, linearly polarised radiation. At angles in between, elliptically polarised.

Question 10

Describe the polarisation of synchrotron radiation.

Answer 10

Beaming if emission from relativistic particle means emission only detected when particle velocity points (nearly) towards us. Electron only seen at same point throughout its orbit, when acceleration is in same direction. E field in same direction as acceleration, highly linearly polarised radiation. Not totally linear as electron with pitch angles within range 2/gamma will radiate in our direction. Gives small component of circular polarisation

Question 11

What is the Brightness Temperature?

Answer 11

The temperature that a black body would have to have to give the same intensity of emission at that frequency

Question 12

Describe synchrotron self absorption.

Answer 12

Defined the spectrum of a synchrotron emission as a power-law S_nu is prop to nu^-alpha and so as we move towards lower freqs, the effective temp of radiation will exceed the effective temp of the radiating electrons. According to the principle of detailed balance, every emission process has an associated absorption process. If there is more energy in radiation than emission, electrons will absorb energy

Question 13

Describe how the self-absorbed spectrum behaves

Answer 13

Initial rise with nu^(5/2) followed by a turnover and a decrease with nu^(-alpha)

Question 14

When is the total energy in B and relativistic electrons a minimum?

Answer 14

Corresponds to equipartition of energy between electrons and the magnetic field

Question 15

What is Compton Scattering?

Answer 15

The scattering of a high-energy photon by a charged particle (usually an electron)

Question 16

How does Compton Scattering differ from Thomson Scattering?

Answer 16

In Thomson scattering the photon has its direction changed but the energy remains the same. In Compton Scattering the energy of the photon approaches the rest-mass of the electron, the scattering interaction can change the momentum of the photon, meaning the photon loses energy to the particle.

Question 17

What is Inverse Compton Scattering?

Answer 17

The scattering of low-energy photons by high-energy electrons, producing a high-energy photon and a lower energy electron.

Question 18

What is the electron energy loss rate for ICS?

Answer 18

-dE/dt = (4/3)(γ^2)(U_photon)(σ_Τ)c

Question 19

Why is U_B changed to U_photon when calculating the energy loss rate for ICS when compared to Synchrotron?

Answer 19

The electron only cares about the acceleration (ie E) in its rest frame

Question 20

Why are the energies between ICS and synchrotron radiation different?

Answer 20

There is a max energy photon, of energy 4(γ^2)hν, arising from head-on collision, which is a strict upper limit.

Question 21

For what values of b (b=B/10nT) does ICS dominate?

Answer 21

b«0.03, for b»0.03 synchrotron losses dominate.