Are Adiabatic Invariants Violated for 10 keV Electrons During a Substorm?

[Raptor112]

Homework Statement

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
$\tau_{ disturbance} / \tau_{ invariant} >>10$

Homework 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 $= \frac{qB}{m}$

The Attempt at a Solution

Not sure what value of $\alpha_{eq}$ to use?

 

[jasonRF]

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