THE DST EFFECT

The Dst effect results from the adiabatic response o f electrons to changes in the Earth’s magnetic field strength, usually associated with the intensification o f the ring current during the main phase o f a magnetic storm. If the temporal and spatial variations in the Earth’s magnetic field occur on scales that are large compared with the scales associated with the electrons’

adiabatic invariants, then the invariants will be conserved. As the main phase o f a magnetic

storm progresses, an electron experiences a decrease in the local magnetic field strength. Thus, if the electron’s first adiabatic invariant, M, is conserved, then the electron’s kinetic energy will

also decrease. Conservation o f the second adiabatic invariant, J, requires that the integral o f the

electron’s parallel momentum along the bounce path o f the electron remains constant. Thus

during a decrease in the Earth’s magnetic field strength, as the electron moves out to a larger drift shell, the electron’s mirror points must move to higher altitudes to conserve the value of

the second invariant, J. The third adiabatic invariant, d>, aims to conserve the magnetic flux

through the electron’s drift shell. During the onset o f a magnetic storm the decrease in the

Earth’s magnetic field strength within the electron’s drift shell will cause the electron to move outward in order to enlarge its drift shell and thus keep the total magnetic flux through the drift shell constant.

Thus the global effect during the decrease in the Earth’s magnetic field is a systematic shift to

larger L shells and a drop in the kinetic energy o f all the electrons. Using an approximate

model by Roederer, [1970], which relates Dst to the particles’ adiabatic invariants, we can

model the adiabatic behaviour o f electrons during magnetic storms.

A crude model o f the Earth’s magnetic field in the equatorial plane during magnetic

disturbances, such as magnetic storms, determined by Roederer [1970] is given by;

B {r) = ^ - k , ( t ) f o r r S 4 - 5 R E

Here ko = 8xlO'^ T m^, represents the Earth’s magnetic dipole moment and A:i(t) ~ Dst is a

measure o f the contribution o f the ring current. If a simple dipole magnetic field is assumed then the equatorial drift paths remain circular at all times. For a particle with energy 7] prior to

the magnetic disturbance that is drifting at a radial distance r, where the magnetic field is the

C h a p te r 4 - R e la tiv is tic E lectron Flux E n h a n c e m e n ts

During the disturbance the flux through the instantaneous guiding drift path must remain equal to O, thus;

r{t)

However, because in general k\ « {ko/r^) the radial distance o f the guiding drift path at time, t

during the disturbance can be expressed as;

r(t) = r. +Ar

2

The magnetic field strength as seen by the electron is then given by;

B(t) = Bj +AB

AB = ---(/)

2 ’

The electron’s kinetic energy during the disturbance can now be determined firom the equation o f the electron’s magnetic moment and the fact that the electron’s first adiabatic invariant is conserved to give;

Figure 4.2-2 shows the variation in location and energy o f IMev electrons during successive

magnetic storms that occurred during the first six months o f 1995. This illustrates the

importance o f making comparisons between the measured electron flux at times of near to equal Dst if we intend to identify non-adiabatic processes, such as loss or heating o f electrons, during magnetic storms. The significant change in the electron’s location and energy during magnetic storms needs to be accounted for while studying the behaviour o f the relativistic electron

population. For example, the large drop in the electron energy during the main phase o f the

magnetic storms would be seen as a large and rapid drop in the flux levels detected by a fixed minimum energy threshold detector.

C h apter 4 - R e la tiv is tic E lectron Flux En hancem ents U J V —I Tf % -> <B

II

’u] UO U O IA I Oiieqeipv [A8|M] UOJJO0I3 a9^\1 L

E J O i s u o n e u B A

A6j8U3 oiiBqeipv

F ig u re 4.2-2 T he a d ia b a tic re s p o n s e o f 1 MeV e le c tro n s d u r in g su c c e ssiv e m a g n e tic s to rm s , also k n o w n as th e D st effect.

C h a p ter 4 - R e la tiv is tic Electron Flux E n hancem ents

If during a magnetic storm the three adiabatic invariants associated with each electron are conserved at all times, then as Dst returns to near to zero nano-tesla, the electrons will also

return to their original energy and location. However, it should be noted that the Dst effect

requires that all three invariants remain conserved throughout the magnetic stonn, criteria that are not always met during the storm main phase. Effects such as wave-particle interactions in the form o f pitch angle scattering lead to the violation o f the invariants. Also during the main phase o f magnetic storms a significant fraction of electrons are thought to be permanently lost. However, it is not known what proportion of the flux decrease during the magnetic storm main

phase is due to the Dst effect or to electron loss. In addition, it is not clear whether a

subsequent recovery o f the electron flux to pre-storm levels, during the magnetic storm recovery

phase, is a result of the Dst effect or due to electron acceleration. The only way to compare

flux measurements taken at different times, while ruling out any differences due to the Dst effect, is to make the measurements at times o f close to equal Dst as indicated in Figure 4.2-3.

Pre-storm Post-storm UJ Time in Days F ig u re 4.2-3 P re -sto rm , p o s t-s to rm c o m p a ris o n o f th e REC u s e d fo r th e c la s s ific a tio n o f e v e n ts.

This method allows us to rule out changes in the measured electron flux due to the electrons’ adiabatic response to changing magnetic field conditions during the storm. Hence the only way to be sure that electron acceleration has taken place is if the electron flux enhancement during the recovery phase exceeds the pre-storm flux level at times o f approximately equal Dst.

C h a p te r 4 - R e la tiv is tic E lectron Flux E n h a n cem en ts

4.3 DATA