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
6
Order by Order with ⌫̇/⌫ ⌧ 1
7
Order by Order with ⌫̇/⌫ ⌧ 1
but, how does energy and amplitude change with frequency?
8
Understanding the Energy/Amplitude
9
Understanding the Energy/Amplitude
10
Understanding the Energy/Amplitude
11
Hamiltonian for an Oscillator
12
Hamiltonian for an Oscillator
13
Hamiltonian for an Oscillator
14
How Good are Adiabatic Invariants?
15
How Good are Adiabatic Invariants?
Answer:Exponentially good
16
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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
17
Drift Hamiltonian
18
Examples of Confined Orbits (Part 2)
19
Toroidal Magnetic Field
20
Toroidal Magnetic Field|B| varies along the magnetic field
21
Toroidal Magnetic FieldTrapped and Passing Particles
22
Toroidal Magnetic FieldHow Many Trapped Particles?
23
Toroidal Magnetic FieldBounce Motion
24
Toroidal Magnetic FieldDrift Motion
25
Toroidal Magnetic FieldDrift Motion
26
Toroidal Magnetic FieldBanana Orbits
27
Toroidal Magnetic FieldPassing Orbits
Only here…
28
Depending upon turning point, toroidal drift reverses!
Toroidal Magnetic FieldToroidal Precession Frequency
29
Next Lecture
• Piel / Chapter 4: Stochastic Processes in Plasma