Robert Winglee, Space Sciences Editor
American Geophysical Union
2000 Florida Avenue, N.W.
Washington, D.C. 20009
Telephone(202)462-6910 ext.326
Fax (202)462-2253
Editor's Assistant:

October 6, 1997

Dr. Robert B. Sheldon
Center for Space Physics
Boston University
725 Commonwealth Ave
Boston, MA 02215

Re: "On the physical origin of outer radiation belt 1-10 MeV electrons"

Dear Dr. Sheldon:

We have sent your paper to two referees, whose reports are enclosed. As you can see, both referees are favorable towards the results and particle tracking components, but both have major concerns about the section on cusp acceleration, which is preventing publication at this stage. If you were to increase emphasis on the results of the first two sections, while keeping the pertinent physics in the theory and removing speculations, we might be able to move in a more positive direction.

The paper is not, in its present form, acceptable for publication in Geophysical Research Letters. However, if you wish to submit a revised paper that may be sent out for further review, you should respond specifically to the referee's questions and comments in your cover letter.

Please send four copies of your revised paper to Maura T. C. Wright, Editor's Asistant at the above address by October 29, 1997. If you cannot respond within this time frame, or if you do not plan to submit a revision, we would appreciate you letting us know.

for Robert Winglee
Space Sciences Editor

via Maura T. C. Wright
Editor's Assistant

Referee A

Review of "On the Physical Origin and Prediction of Killer Electron Storms" by R. B. Sheldon et al.

In my original review, I raised 4 main objections. I find that the authors have satisfactorily addressed only half of these in the revised manuscript. Below I comment on these objections, assigning the same number to them as in the original review.

1. The style of this manuscript has improved considerably. The inappropriate sensationalism that permeated the original version has been removed. I no longer have any objections to the style of the presentation.

2. The reference to the Telstar failure has been removed. The authors now focus on presenting their POLAR observations and theory.

3 and 4. In the first three sections of the manuscript, the authors present observations and simulations which support an electron population being trapped in the outer cusp. Aside from a few new comments that I explain later, I do not have any major objections about the first three sections of the paper. In the cusp acceleration theory section, the authors present a very simplistic argument that the electrons trapped in the cusp can get energized to ~1 MeV and can escape the trap to diffuse into the radiation belts. The section is simply a discussion of a hypothesis. Any one can hypothesize or theorize anything they want. However, if one wants others to publish their hypothesis or theory in a scientific journal, one must provide reasonable evidence for it. I am not asking for irrefutable proof. i am asking for further analysis either in the form of observations, theoretical analysis, or numerical simulations that shows that this energization and untrapping process can happen under the reasonable magnetospheric parameters. Since the authors invoked simulations of electron trajectories in the Tsyganenko 1996 magnetic field model, using simulations to show the energization and untrapping would be a logical approach. That is why I suggested it. However, other approaches are acceptable.

Thus, my original objections here still stand. There is a lack of systematic and serious analysis presented in this manuscript ot support their cusp acceleration theory. However, half the focus of this paper is on their cusp acceleration theory. One suggestion is to shift the focus of the paper toward more observational anlysis of the electron population in the cusp region. Another suggestion is to include further analysis (theory, simulations, or data analysis) that shows what population of electrons (range of initial energies and initial pitch angles) can gain sufficient energy in the cusp to escape the trap to populate the outer radiation belt. Until a serious revision such as suggested is made, I do not recommend publication of this manuscript in Geophysical Research Letters.

New Comments:

1. Introduction, paragraph 3, lines 1-3: Your explanation of Selesnick and Blake's [1997] paper in your reply was better and more fair than what you wrote here. You need to state here that the phase space density at constant magnetic moment uniformly rises toward higher L-shells during quiet times (but not during active times). You left out that key point.

2. Data Analysis Section, paragraph 2, lines 7-8: In Figure 1 the radiation belt fluxes look more isotropic than the cusp fluxes. This needs clarification.

Referee B

Report to Authors

The most troublesome part of the paper is the section on "A Theory of Cusp Acceleration". I believe that the argument described in the first paragraph and upon which the section depends is incorrect. If a charged particle moves in static electric and magnetic fields while experiencing elastic scattering, its energy after moving from r0 to r1 is E(r1)=E(r0) + q[V(r0) - V(r1)], where V(r) is the electrostatic potential at r. This result is independent of the path, number and sequence of collisions, etc. In the example of "magnetic pumping" given, the particle will indeed gain energy in the first 180 deg drift. This energy will be lost on the return trip ascending the potential. If scattering reduces the pitch angle and therefore the magnetic moment, the particle will not be able to climb the potential to the starting point. It will return to a lower potential point near the starting position. If the magnetic moment after scattering is too small, the particle will not complete a loop but will E X B drift out of the region. In any case a particle cannot cumulatively gain energy by recirculating as described. The energy will always be given by the above expression no matter how many cycles are made. The magnetic pumping process referred to by the authors' (such as described by Alfven and Falthammer) involves quite different circumstances, i.e. changing magnetic or electric fields.

Other comments:

1) In the abstract it is stated that POLAR observed increases in cusp electrons which preceded electrons seen at geosynchronous altitude. This point is not discussed in the paper except on page 7--8 the authors say they will make this comparison in a future study.

2) Figure 1 needs a caption. I was unable to make the phase space comparisons as my copy was not in color. I assume the comparisons described in the text are valid.

4) Table 1. "MeV" should be "keV". Also I suspect mu is not relativistically correct as it assumes p2 is proportional to Energy. I am surprised the bounce period does not depend on local time.

5) On page 7 the mirror equation should have sin's squared.

6) Page 3. Selescick and Blake did not see phase space densities uniformely rising with L. Because of the sporadic substorm injections, their data show a variety of shapes including phase space density maxima at L~5.


Dr. Robert Sheldon
Center for Space Physics
Boston University
725 Commonwealth Av
Boston, MA 02215

Robert Winglee
Geophysical Research Letters
University of Washington
Seattle, WA

Dear Dr. Winglee,

I have carefully read the referee comments, and am encouraged that they find no fault with the observational first half of the paper. I am also quite flattered to have achieved an informal reporting style, it has been quite difficult to accomplish. However I am troubled that they believe a pure observational result is of greater value than one having both observations and explanatory discussion. (I regret having called such speculation a theory, it is more properly simply a discussion.) I believe these results are only marginally valuable unless the discussion and data are presented together. Thus I will do my best to satisfy Referee A that the speculation is much further developed than he suspects, and I will plead with Referee B to overlook my faux pas in conflating two separate acceleration mechanisms into one, and to regard the discussion section as still relevant. Clearly the resistance to this work centers on the discussion section, which we address at length below, however I will address the issues in the order in which they were presented in the referee reports.

Referee A.

Old 3+4: ``I am asking for further analysis...that shows that this energization and untrapping process can happen under the reasonable magnetospheric parameters.''


The process of untrapping can be divided into 2 categories, static and dynamic. Static untrapping occurs when adiabatic particle drifts put the particle in a location where one of the adiabatic invariants breaks down. The drift loss cone of Roederer 1970 is such an example. Dynamic untrapping occurs when a time-variable system destroys one of the adiabatic invariants, pitch-angle scattering into the loss cone is an example. We consider both in detail below:

a) Static

Our mapping of particle trajectories in a 1996 Tsyganenko magnetic field shows that the radial limit of stable trapping shrinks with energy. Defining this radial limit as the cusp ``L-shell'', the distance of the ``cusp equator'' (defined in the text as the tangency of the field line with the curves of constant |B|-magnitude) from the center of the cusp (defined as the minimum |B| point near the magnetopause) we can show that the ``hole'' in the center of the cusp, where particles are untrapped due to the extreme curvature of the field line passing near the center of the cusp, expands with energy. Simultaneously the largest cusp L-shell decreases with energy, so that the annulus of trapped cusp L-shells shrinks in area with increasing energy, eventually shrinking to zero area at around 5 MeV. The reason for this is obvious, as the gyromotion of the particles becomes comparable to the cusp size, it no longer is trapped by the cusp gradients.

I have generated several gigabytes of trajectory files (which were used to make figure 2.) and from which I have obtained this result. It was gratifying to see that limit of E>5 MeV untrapping corresponds very well with the 2 MeV cutoff visible in the data. However the presentation of these results appears to be too lengthy for the space available in this GRL manuscript. If I can beg the referee to accept it on faith, I will elaborate in much greater detail in a second publication.

b) Dynamic

Invoking pitch-angle scattering as an untrapping mechanism is always possible, particularly in the cusp with its large broadband electromagnetic noise spectrum. This is particularly valid because a particle with a 60 degree pitchangle in the cusp will have a much more trapped ~90 degree pitchangle in the tail, owing to the large increase in magnetic field seen between the cusp and the drift-orbit connected location in the tail. That is, the cusp-loss cone is the dipole-trap, not the dipole-loss cone. However we prefer to discuss the dynamic untrapping of the mirror-point magnetic field. That is, the effect of weakening the magnetic field strength near the nose of the magnetosphere. The first mechanism would produce a steady drizzle of energetic particles into the quasi-trapping regions near the nose of the magnetosphere. The second mechanism would produce a veritable flood.

The first mechanism might explain the radial profiles of the radiation belts during ``quiet'' periods. The second would explain the sudden increases typified by the January 10, 1997 storm. Since the existence of pitch-angle scattering is well accepted, I will suppose that the referee will grant me a steady drizzle. Turning my attention then to the flood, we need to consider carefully what happens to a trapped particle when the boundary conditions are changed rapidly, i.e., do the particles stay fixed in space and the field-lines change their mapping, or do the particles follow the rapidly moving field line?

We can sidestep some of this difficulty by recognizing that a particle undergoing a ``bounce'' is following an L-shaped trajectory that is both perpendicular and parallel to the magnetopause. The magnetopause responds to a sudden decrease in SW pressure by retreating outwards and simultaneously decreasing its Chapman-Ferraro currents. Now when the trapped particle is closest to the earth, it is on a field line essentially perpendicular to the magnetopause. Thus cusp currents do not to first order affect the field line on which the particle is gyrating. Rather, the circular currents on the magnetopause form a dipolar field that decays rapidly with distance and to second order imperceptibly weakens the |B|-magnitude of the field-line on which the particle is gyrating. Thus we are safe in saying that the sudden decrease in SW pressure to first order has no effect on this class of particles.

Now as this particle moves along its field line out toward the cusp, it finds that the cusp has retreated, but nonetheless passes the cusp with slightly smaller pitchangle and moves outward along the magnetopause (see the lily-orbit plot). However the weaker C-F currents in the magnetopause, (which create the dayside maximum to first order), make too small an increase in the field to force this particle to mirror, and so it is lost to the cusp and rejoins the dipole trap particles. Thus motions of the magnetopause can untrap particles on a bounce timescale, leading to a flood of exiting particles.

One hardly needs to run the T96 code to make the discovery that the dayside maximum in the |B|-magnitude is dependent on SW pressure. Thus I have merely claimed this result without plotting it.


The evidence that energization is occurring is inescapable, with phase space densities in all regions surrounding the cusp lower than the cusp, it is clear that the cusp must energize the particles (or violate diffusion). The ability for fluctuations to energize particles is well accepted in the trapped dipolar regions of the magnetosphere (e.g. radiation belt diffusion), so I would suppose that the referees have no difficulty in accepting standard resonant acceleration mechanisms once they accept the existence of the three adiabatic invariants. On the other hand, the proposition of chaotic acceleration requires some further elaboration.

I have shown a table of adiabatic periods of the motion in and around the cusp. We have also plotted (but not displayed) the magnetic power spectra from the POLAR/MFE magnetometer taken during cusp passes that show both large power and peaks (~100 mHz) in this frequency range. However I find this evidence inconclusive since it is well known that the cusp is a region having broadband noise (one of the best ways to identify the cusp before POLAR/PWI failed). Nor is there a well-established lower limit on the size of the fluctuations needed to drive the diffusion. Nor have their been correlations between the degree with which the resonances overlap with the magnitude of the fluctuations needed to drive the orbits chaotic. In short, I cannot present a complete theory of chaotic acceleration in four pages, nor, I believe in 11 pages of JGR, but I CAN show that the conditions in the cusp are completely applicable to the theory.

Since there is a shortage of alternative theories of ORBE acceleration, it would appear to me that the burden of proof is considerably lightened E.g., an initial discovery paper need not be the final word on the subject, only that it present an observationally consistent theory that in relation to its competition, deserves mention. Thus my goal is merely to show that the speculation is observationally consistent. In view of the Referee's objection, I have attempted to indicate that this is a speculative agreement.

New Comments:

1) Selesnick?

I have modified the text to be in better agreement with both Selesnick's paper and my deductions.

2) Isotropic?

I concluded that this was difficult to show from my data presentation and completely extraneous to the argument. So I have deleted it.


Referee B

0) Magnetic Pumping?

The Referee is entirely correct in rejecting my previous draft. I had never intended to include a section on ``resonant acceleration mechanisms'' but being prompted by the referee I added this section too quickly, erroneously conflating a Bohm-diffusion mechanism with a magnetic pumping mechanism, which I had thought was applicable to both. Please overlook my previous explanation, and try to give the present explanation a fresh reading. The sole purpose of this paragraph is to demonstrate by way of example a type of resonant acceleration, since resonant processes are commonly applied to trapped particles. They are also well accepted mechanisms for violating the three adiabatic invariants.

( beginning of parenthetical remarks)

For the sake of my pride, the mechanism I described though not ``magnetic pumping'' works as follows:


1) Three adiabatic invariants, e.g., Closed drift orbits are present.

2) Large scale electric field (scalar potential) is present.

Then the corollaries to this are:

3) the total energy can be represented by Ho = mu Bm + q U

where mu is the first invariant, q is the charge, Bm is the mirror point magnetic field strength, and U is the electrostatic scalar potential.

4) Then drift from point P to point Q, say, into a region of smaller U requires larger Bm such that mu Bm(P) + qU(P) = mu Bm(Q) = qU(Q)

5) Pitch-angle scattering changes mu but in such a way that mu * Bm = constant

Now let us use this information in an example:

1) Let point P and Q be two locations in a trap (dipole or cusp) with a linear potential field and circular |B| potentials.

2) Let Q be such that it is a tangency point between constant |B|-surfaces and constant U surfaces. Travel from the tangency point along surfaces of constant U leads to weaker |B| in the case of a dipole, but stronger |B| in the case of a cusp trap.

3) Let the particle begin with Bm=B0 e.g. a 90 degree pitchangle at point P with higher U and drift toward Q at lower U. U(P)>U(Q).

4) Motion from higher U(P) to lower U(Q) requires Bm(Q) to be larger. In the cusp, this means that the cusp L-shell is increasing. E.g., the particle spirals outward.

5) At point Q, let pitch-angle scattering reduces mu to an arbitrarily small value, increasing Bm to a very large value. (e.g., converting E-perpendicular into E-parallel.)

6) Let the particle then drift from point Q to point R.

7) From the energy equation, one can see that for very small values of mu, the particles essentially remain at constant U. At point Q, this implies that the particle must drift to a region of stronger equatorial |B|-magnitude. |B_0(R)| > |B_0(Q)|

8) Let pitch-angle scattering then change the pitch-angle entirely back to 90deg particles. We argue that mu Bm(R) > mu Bm(Q).

1b) Now let the particle drift from point R to S, where S is a tangency point like Q. The system can then continue back at step 4, tracing out a zig-zag path as it diffuses in L-shell and gaining energy.

In this way, a particle can zig-zag toward larger Bm, without the need for a fluctuating electric field which spirals the particles outward, picking up energy in the process. The purpose of this demonstration was to show that violation of any of the adiabatic invariants can be used to accelerate particles.

(end of parenthetical remarks)

1) Cusp preceding belt?

The observations of cusp particle enhancements preceding belt enhancements in the abstract are valid, though clearly require additional work in the text. They were observed using movies of the cusp and belts, which is quite difficult to reproduce in the text. I have used multiple frames from the movie to make this point, but at a cost of a lot of real estate in an already crowded GRL.

2) Caption to figure 1?

There IS a caption, which refers to the text. Since the description of this data is crucial to the flow of the argument, it made more sense to include it in the body of the text. For the sake of brevity, it was not duplicated in the caption.

4) MeV?

The error is mine. keV was meant. The energies were corrected for rest mass, e.g., the particle trajectories were traced with a proper relativistic velocity. Mu was taken to be the ``natural'' non-relativistic value, e.g., the perpendicular component of energy as would be measured by a solid-state detector. This was not corrected for relativistic mass changes. It would be easy to redefine it, though for illustrative purposes, its exact value is of lesser interest than its magnitude.

5) sin^2

It has been corrected.

6) Selesnick?

The comments here are similar to those of Referee A. Please read the referee A comments first.

Referee B gives an interpretation that does not exist in the Selesnick paper itself. Referee B interprets the ``variety of shapes'' to be ``because of the sporadic substorm injections''. The connection of substorms to outer radiation belt injections is not made in the paper itself, Selesnick carefully avoids using the word ``substorm'' anywhere. I hope that the Referee merely meant ``particle injections'', in which case I am in complete agreement with the referee. I have tried to clarify my position: a time-variable external source, which I reiterate, is in complete agreement with Selesnick and Blake.

Let me restate this. If one posits an internal source (a local acceleration that generates a peak in the trapping region, 210. Since decay is constantly occurring, the quiet-time signatures must represent a steady source and not just a transient decay signature, since the steady-state for a sourceless population is zero flux. Therefore, if one posits an internal acceleration mechanism for storms, one must posit a second, external acceleration mechanism to explain the quiet-time fluxes.

A single external, time-variable source can account for both storms and quiet periods. Therefore by Occam's Razor (what can be done with fewer assumptions is done in vain by more), a single source appears preferable to a double source.

Sincerely, Robert Sheldon