Lecture4: Plasma Physics 1

APPH E6101x Columbia University

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Outline• Charged Particle Drifts (Summary)

• Adiabatic Invariants (Part 1)

• Examples (Part 2):

• Mirror

• Magnetosphere (dipole)

• Tokamak

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and for trapped particles with ρ/L << 1, (µ, J, Φ) ~ adiabatic invariants

Gyro Motion (Summary)

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Adiabatic Invariants (Part 1)

(µ, J, )

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Harmonic Oscillator• Separate descriptions of perpendicular and parallel motion

• Fast gyration around B

• Slow perpendicular drift of gyro center

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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

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