Lecture4: Plasma Physics 1 APPH E6101x Columbia University 1
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Lecture4: Plasma Physics 1
APPH E6101x Columbia University
1
Outline• Charged Particle Drifts (Summary)
• Adiabatic Invariants (Part 1)
• Examples (Part 2):
• Mirror
• Magnetosphere (dipole)
• Tokamak
2
and for trapped particles with ρ/L << 1, (µ, J, Φ) ~ adiabatic invariants
Gyro Motion (Summary)
3
Adiabatic Invariants (Part 1)
(µ, J, )
4
Harmonic Oscillator• Separate descriptions of perpendicular and parallel motion
• Fast gyration around B
• Slow perpendicular drift of gyro center
5
What happens when ω(t) changes slowly with time?
• Separate descriptions of perpendicular and parallel motion
• Fast gyration around B
• Slow perpendicular drift of gyro center
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Order by Order with ⌫̇/⌫ ⌧ 1
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Order by Order with ⌫̇/⌫ ⌧ 1
but, how does energy and amplitude change with frequency?
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Understanding the Energy/Amplitude
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Understanding the Energy/Amplitude
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Understanding the Energy/Amplitude
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Hamiltonian for an Oscillator
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Hamiltonian for an Oscillator
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Hamiltonian for an Oscillator
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How Good are Adiabatic Invariants?
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How Good are Adiabatic Invariants?
Answer:Exponentially good
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This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:128.59.150.139 On: Mon, 21 Sep 2015 16:47:53
This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP:128.59.150.139 On: Mon, 21 Sep 2015 16:47:53
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Drift Hamiltonian
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Examples of Confined Orbits (Part 2)
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Toroidal Magnetic Field
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Toroidal Magnetic Field|B| varies along the magnetic field
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Toroidal Magnetic FieldTrapped and Passing Particles
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Toroidal Magnetic FieldHow Many Trapped Particles?
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Toroidal Magnetic FieldBounce Motion
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Toroidal Magnetic FieldDrift Motion
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Toroidal Magnetic FieldDrift Motion
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Toroidal Magnetic FieldBanana Orbits
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Toroidal Magnetic FieldPassing Orbits
Only here…
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Depending upon turning point, toroidal drift reverses!
Toroidal Magnetic FieldToroidal Precession Frequency
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Next Lecture
• Piel / Chapter 4: Stochastic Processes in Plasma
• Distribution function
• Collisions
30
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