Solution-One-dimensional vlasov equation

One-dimensional vlasov equation

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Reference no: EM13316818

1. THE VLASOV EQUATION

Show that the one-dimensional Vlasov equation,

2453_Vlasov equation.png

can be obtained by Taylor expansion of the right-hand side of:

2443_Vlasov equation1.png

2. ISOTROPIC PRESSURE

Show that the off-diagonal terms of the pressure tensor

2442_Vlasov equation2.png

vanish if f¾ is an isotropic function of ±v (i.e., randomization is the same in any direction). Hint: Expand the the tensor ±v ¢±vf¾ and integrate terms individually (you need only do this for one diagnoal term, and one off-diagona, and argue similarity with other tensor terms).

3. ACCELERATION TERM IN THE VLASOV EQUATION

Show that the acceleration integral in the ?rstmoment of the Vlasov equation gives

563_Vlasov equation3.png

Hint: Integrate by parts, taking into account that

284_Vlasov equation4.png

Reference no: EM13316818

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One-dimensional vlasov equation

Reference no: EM13316818

Reference no: EM13316818

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