Multi-beams simulation in PIC1D

Hands-on section 4

Initialization in velocity of multi-beams

Lorentz distribution:

( ) ( )lorentz uniformp v dv p v dv

The density of probability is equal for any distribution:

2 2

1

( )

tan( ( 0.5)) .

vB

uniformD B

uniform B D

vdv P

v v v

v P v v

We can use this result to initialize v of particles and use some differentvb and vd to get multi-beams. Then we do similar things like hands-onsection 2.

1D Vlasov-Poisson equations

Equation of PIC weight

Flow chart of PIC1D

Push particles with the equation of motion

Set the initial conditions Mainly (x, v)

Gather particles into gridand calculate the electric

field E.

PIC method

Locate E into ever particle

t = t + dt

end

t = t (end)

Plot of 2 beams in phase space

Plot of 5 beams in phase space