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Violation of Adiabatic Invariances

  1. Feb 10, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider the following disturbances. Clearly state for 10 keV electrons if any of the three adiabatic invariants violated, and justify your answer?
    (i) The magnetic field at L = 6.5 (~geo-stationary orbit) steadily changes strength and direction from one state to another in a time of less than 40 minutes during a substorm.
    Hint: the condition for non-violation is that ##\tau_{ disturbance} / \tau_{ invariant} >>1 ##
    It is useful to quantify “>>” : for this problem sheet please express the condition as
    ##\tau_{ disturbance} / \tau_{ invariant} >>10 ##

    2. Relevant equations
    Bounce Period ## = L R_{E} (\frac{W}{M})^{-0.5}(3.7 -1.6 sin(\alpha_{eq}))##
    Drift Period ## = \frac{{2}q B_E R_E ^2}{3LW}\frac{1}{0.7+0.3sin\alpha_{eq}}##
    Gyro Period ## = \frac{qB}{m}##

    3. The attempt at a solution
    Not sure what value of ##\alpha_{eq}## to use?
     
  2. jcsd
  3. Feb 12, 2016 #2

    jasonRF

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    Science Advisor
    Gold Member

    What are the two extremes for the periods of interest (ie when the sin term is +1 or -1)?
     
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