Violation of Adiabatic Invariances

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In summary, the conversation discussed the violation of adiabatic invariants in the presence of disturbances, specifically for 10 keV electrons. The condition for non-violation was stated as ##\tau_{ disturbance} / \tau_{ invariant} >>10 ## and the equations for the bounce period, drift period, and gyro period were provided. The value of ##\alpha_{eq}## to use was not specified, but the extremes for the periods of interest were mentioned to be when the sin term is +1 or -1.
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Raptor112
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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?
 
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  • #2
What are the two extremes for the periods of interest (ie when the sin term is +1 or -1)?
 

Related to Violation of Adiabatic Invariances

1. What is adiabatic invariance?

Adiabatic invariance is a principle in physics that states that certain physical quantities remain constant during an adiabatic process, where there is no heat exchange between the system and its surroundings. These quantities include energy, momentum, and angular momentum.

2. What causes a violation of adiabatic invariance?

A violation of adiabatic invariance can occur when there is a sudden change in the system or when the adiabatic process is not perfectly isolated. This can happen due to external forces or interactions with other systems.

3. What are the consequences of a violation of adiabatic invariance?

The consequences of a violation of adiabatic invariance can vary depending on the system and the extent of the violation. In some cases, it can lead to a change in the energy or other conserved quantities of the system. It can also affect the stability and behavior of the system.

4. How can a violation of adiabatic invariance be avoided?

To avoid a violation of adiabatic invariance, it is important to ensure that the adiabatic process is as isolated as possible and that sudden changes are minimized. This can be achieved by carefully designing and controlling the experimental setup, and by using adiabatic shielding techniques to reduce external influences.

5. Can a violation of adiabatic invariance be beneficial?

While a violation of adiabatic invariance is generally undesirable in scientific experiments, it can also have some beneficial effects. In some cases, it can lead to new discoveries or unexpected results that can further our understanding of a system. However, it is important to carefully analyze and understand the consequences of such violations in order to properly interpret the results.

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