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Propagation of laser pulses in plasma

Introduction

Nonlinear equation describe propagation of ultrashort laser pulses in plasma, see report of D. Jovanovi\'c and R. Fedele.

Equation to solve


2iA(x,y,z)

t
+ ∆A(x,y,z) + Φ(x,y,z) A(x,y,z) = 0
where
Φ(x,y,z) = 1

2



z 
sin(zz′)|A2(x,y,z′)|dz′.

Domain

Rectangular parallelepiped [−40,40]×[−40,40]×[−16,16].

Mesh

x=∆y=2, ∆z=0.4, ∆t = 0.0005.

Initial condition

The function at zero time is asymmetric Gaussian,
A(x,y,z) = 5e−0.01 x2−0.01 y2z2.

Boundary conditions

Periodic boundary conditions.

Calculations

Used Mathematica program.

Results

results.jpg

Change of A with time.
phi.jpg

Change of Φ with time (animation).

Animation

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