Particle acceleration

Question 1

What key comparative element do we use to know if an object can accelerate a particle to a speed close to the light speed?

Answer 1

We use the Schwarzschild radius
If a star isn’t much larger than its Schwarzschild radius, it will accelerate particle to a speed close to the speed of light.

Question 2

A free particle falling from infinity will adquire a velocity v(r) = ?

Answer 2

v(r) = sqrt(2GM/r)

Question 3

Relativistic speed means that v is close to c, thus v/c = ?

Answer 3

v/c = sqrt(Rs/r)

Question 4

Expression of the Schwarschild radius?

Answer 4

Rs = 2GM / c^2

Question 5

At what condition is an electric field able to cause particle acceleration?

Answer 5

In an electromagnetic field, particle acceleration can only work when an elecric field exists along magnetic field lines. Turbulent and random magnetic fields are expected to produce such acceleration mechanisms.

Question 6

Example of extrem electromagnetic accelerators ?

Answer 6

Pulsars are examples of extrem electromagnetic accelerators where electrons reach Lorentz factors up to 10^9.

Question 7

What is Second order Fermi acceleration ?

Answer 7

Particles acceleration due to scattering by fluctuation in the magnetic field.

Question 8

What was Fermi the first to propose ?

Answer 8

Production of CR by scattering of particles between molecular clouds.

Question 9

Is Second order Fermi acceleration efficient ?

Answer 9

Yes is can be efficient, but not for relativistic particles.

Question 10

What is First order Fermi acceleration ?

Answer 10

Particle acceleration due to collision with a strong shock wave

Question 11

How come with First order Fermi acceleration we always get “lucky”?

Answer 11

It is because at each crossing the particles sees a magnetic wall at V = 1 - 1/r
-> so only heads on collisions