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Lecture4: Plasma Physics 1 APPH E6101x Columbia University 1
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Transcript of Lecture4: Plasma Physics 1 - Columbia...

  • 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

  • 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

  • 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

    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

    • Distribution function

    • Collisions

    30