Static magnetic fields

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paraxial approximation microwave horn
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z
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r
y
j
x
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far field
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Be careful with the procedure of calculating the
limits on the integration this is an anomaly
and it is not a real effect!
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microwave horn
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p. 624
?
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plasma
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Waves in plasmas high frequency
Only electrons can move! Mi gt gt me
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Waves in plasmas high frequency
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Waves in plasmas high frequency
Derive a wave equation ? gt ?pe
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Microwave experiment
resonances
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Waves in plasmas low frequency normalized
variables
Equation of continuity for the ions
Equation of motion for the ions
Electrons can respond quickly to electric fields
and we can assume that their density is given by
a Maxwell-Boltzmann relation.
Poissons equation
Electrostatic approximation
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Waves in plasmas low frequency
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Linear experiments

• Vacuum chamber to reduce collisions
• plasma creation
• Ion acoustic wave excitation, propagation, and
  detection

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Waves in plasmas low frequency
???
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Nonlinear fluid equations for ion motion Mel
Widner Ph.D. thesis
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What about the following experiment?
Reflection ???
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Nonlinear ion acoustic solitons

• Scott-Russell experiment 1834
• KdV equation 1895
• Recurrence calculation 1960
• Nonlinear plasma equations ? KdV equation
• Plasma experiments

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Plasma experiment
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Experimental results
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In order to minimize this energy, V must be a
solution of Laplaces equation.
Let there be another solution U that satisfies
the boundary conditions. Linear media implies
superposition!
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Either V is specified (U 0) or the normal
derivative of V 0.