multi-beams simulation in pic1d hands-on section 4
TRANSCRIPT
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Multi-beams simulation in PIC1D
Hands-on section 4
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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.
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1D Vlasov-Poisson equations
Equation of PIC weight
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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)
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Plot of 2 beams in phase space
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Plot of 5 beams in phase space