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June 20, 1997

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

Re: "On the physical origin and prediction of killer electron storms
(GRL ms. #6091)

Dear Dr. Sheldon,

Enclosed are two reviews of your paper. As you can see, both reviewers have a number [of] concerns that would have to be addressed before the paper could be considered acceptable for publication in GRL.

Please consider the reviewers' comments carefully. If you choose to resubmit to GRL, please make the necessary revisions and send your revised typescript (three copies), along with detailed responses to the reviewers, within three weeks. If you will not be able to respond within the requested time, I would appreciate your letting me know as soon as possible.

B. Lewis
for J.H. Waite, Jr.

Referee A

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

This manuscript attempts to address a long-standing unresolved problem of how outer radiation-belt electrons are energized after a magnetic storm. Unfortunately, this manuscript fails miserably to provide a scientific answer to the problem. The author's claim that outer radiation-belt electrons are energized in the cusp region; however, they do not present sufficient evidence to support this claim. The arguments provided are based largely on discussion of general magnetospheric conditions and conjecture of what might have occurred. Furthermore, the style of the manuscript is very sensational, that is it contains many inaccuracies and exaggerations to excite interest. Below I describe in detail my main objections to the manuscript. Also listed are some comments on other errors/inaccuracies in the paper. This list is by no means exhaustive. For all the above reasons, I do not recommend publication of this manuscript in anything resembling its present form in GRL.

Main objections:

1. The manuscript is written in a style that is not appropriate for a scientific journal. It is sensational; that is it contains exaggerations and inaccuracies to excite interest in the subject. Phrases like "killer electrons" instead of energetic or outer radiation-belt electrons are not appropriate. The manuscript in its present form contains statements that one might find in a tabloid or a bad newspaper article instead of a reputable scientific journal. A prime example can be found in the abstract: The loss of the Telstar 401 communications satellite on January 11, 1997, was thought to be due to a deep dielectric discharge (DDD) occurring 24 hours after a sudden, thousand-fold increase in killer electrons. At this time there is NO EVIDENCE that the Telstar satellite failure was due to a deep dielectric discharge.

2. Initially the authors state that the Telstar communications failure may have been due to DDD but then they assume that this is the cause throughout the rest of the paper. At this time there is NO EVIDENCE that the Telstar failure was due to DDD. While it may be possible, it is irresponsible to report this as a fact until evidence has been officially reported. As the authors have pointed out in the introduction, the loss cost (even after insurance) to AT&T may be over $100M. With this magnitude of liability, one should be careful about reporting or publishing statements about the Telstar satellite that cannot be supported by evidence. Thus, I would advise GRL to not publish any such unsupported statements regarding the Telstar failure.**

3. There is insufficient evidence presented here to support the authors' proposal that the energetic electrons of the outer radiation belt are energized in the cusp region. The test particle simulation was performed in the Tsyganenko 1996 model WITHOUT an electric field. The authors themselves claim that a large electric field is necessary for sufficient energization of the electrons. A plot of a representative particle trajectories for 85-keV electrons are shown in Figure 2. However, no quantitative evidence of sufficient energization is presented! The authors conclude that a 5-keV electron is trapped in the cusp for at least 30 minutes based on scaling observations of 500 keV oxygen ions. They should perform test particle simulation with a model electric field and show the trapping time and time history of the particle's energy.

4. The authors' arguments for their proposal of energizing electrons in the cusp consists largely of conjecture. A prime example is in paragraph 2 of page 9: "When the cusp was sufficiently aligned, we surmise that conditions became ideal for the trapping of electrons in the cusp. This trapping, coupled with the large electric fields available at the time, proved to be an efficient mechanism to accelerate the electrons to MeV energies much faster than usual." Where is the proof? Another example is in paragraph 3 of page 9: "We surmise that this fortuitous cusp orientation, coupled with a very slight solar wind shock, produced a much greater than normal trapping of electrons."

Comments on other inaccuracies and ambiguities:

1. Abstract: MeV electrons DO NOT cause single event upsets (SEUs) in logic or memory circuits. Known causes of SEUs include cosmic rays or energetic protons from a proton event.

2. Recent Polar observations of Selesnick and Blake ("Dynamics of the Outer Radiation Belt", to appear in GRL, June 1, 1997) show that phase space density of radiation-belt electrons at constant magnetic moment tends to decrease (rather than increase) with increasing L. This suggests that the sourse is in the trapping region (outward diffusion). This result contradicts the authors' claim in the introduction that the source is external to the trapping region. It also would not be consistent with their proposal of energization in the cusp.

3. Page 8, paragraph 1: What is the definition of a "major killer electron" event? Geosynchronous satellites are periodically exposed to large fluxes of energetic (> 2-MeV electrons) and many do not experience any spacecraft anomalies during these times.

4. There are no units for the fluxes (presumably 1/cm^2-s-ster) in Figure 3.

**After I wrote the review, I learned that Space News has reported that the Telstar communication satellite failure on January 11, 1997 was caused by a hardware problem not deep dielectric charging.

Referee B

"On the Physical Origin and Prediction of Killer Electron Storms"

This is an important experimental paper and should be published. The detection of energetic electrons trapped in the high altitude cusp is an important new result. However, the rather opaque and unconvincing interpretation is a disappointment. Furthermore, the speculative association of these electrons with high energy electrons in the outer belt dominates an otherwise sound experimental result. These thoughts are elaborated below along with some minor corrections. I realize that a GRL paper is intended to be a timely announcement and will not be as complete or rigorous as a full JGR report. Also some of my objections, such as the sensationalism which seeps into the paper, is a matter of taste. Nevertheless, this paper can be improved substantially, and I believe should be altered as discussed below.


The figures are very difficult to read and understand. The numbers on figure 1 required a magnifying glass to read. When printed in the GRL, they will be unreadable. In the bottom panel I assume the unlabeled scale on the right is the radial distance of the satellite. Both L and R are clearly incorrect on the graph. For example at 01:00 L=22.7 and not 35 as plotted. R does not go to zero at 06:15. I am surprised that the slot region shows uup more clearly in the low energy electrons, but perhaps I am missing something. After announcing such an important discovery as cusp trapping, they should give the flux and energy spectrum of this new population. Without knowing the geometric factors of the detectors the community has no way to appreciate or use counting rate information. The energy intervals for each panel are also not given.

Figure 2 also has defects including too small print on the iso-nT contours. The particle trajectories are impossible to follow on my copy of the figure. Perhaps they are easier to see in the color version.

Figure 3 has a caption which is hard to associate with the figure. The caption specifies data for a week, but the data for a month are given. Even with a magnifying glass I can't find a dashed line in either half of the figure, only three dotted lines on the left and two dotted lines on the right half. The vertical scale is undefined. Do actual fluxes of >3 MeV electrons exceed the fluxes of 1.1-1.5 MeV electrons, or is all comparison lost in the scaling?


The abstract emphasizes the "killer" electron problem. Only in the last half of the abstract, and in the fourth line from the the last is the cusp region identified. I would prefer an up-front announcement of the measurement of a new population. The speculation on its importance to "killer" electrons and technology could then follow. I know we are all encouraged by NASA to make spectacular discoveries, but in GRL I prefer to focus on scientific issues.


line 7, 1997-1968=29 years.

page 3 line -7. Reference to the Li et al. (1996 EOS abstract) should probably be changed to the more complete paper by Li et al. GRL 24, 924, 1997.

Page 4, top few lines. They claim to have found the parent population of outer belt MeV electrons. They should at least include the phase space density comparison to support this contention? The reader cannot do this simple calculation as the particle fluxes are not available.

Page 6, The authors do not state that they have traced particle orbits completely around the cusp, a condition needed for long term trapping. One suspects that such orbits exist, although their existence depends on details of the magnetic field. It would be interesting to know if the T 96 field supports long term trapping as well as quasi-trapped orbits.

The last two paragraphs on page 6, continued on page 7, needs elaboration and a clearer explanation as it describes the postulated acceleration mechanism. Non-conservation of the magnetic moment does not change particle energy unless an electric field is present. Scaling residence time to that of O6+ needs justification. However, the main clarification needed is in the description of stochastic acceleration in a static electric field. In particular how does diffusion in a "static" electric field provide 1 MeV of aceleration unless there is a 1 MeV potential difference somewhere in the region? What is the evidence for such large potential drops? At 20 mV/m this field would extend over 50,000 km and require the electron to traverse the entire length.

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

J. H. Waite
Geophysical Research Letters
Southwest Research Institute
PO Drawer 28510
San Antonio, TX 78228-0510

June 20, 1997

Dear Mr. Waite,

I appreciate the concerns expressed in the critique of our paper, and have attempted to address each of these, as noted in the detailed section below as well as in the revised manuscript. However some of the criticism concerned not the content but the style of the presentation for which I take full responsibility, and for which I make no apology. An even more difficult issue for me to respond to were the legal concerns raised by referee A. Both of these issues are peripheral to the scientific discussion, and I am sure that with some help from the referees, we can come to an amicable compromise. I hope that my defense of these issues will not be taken as recalcitrance, but instead as an important apologetic of the role scientists play in shaping society. Thus I have separated the my response into two sections: the first concerning the non-scientific questions, for which I would greatly appreciate an editorial opinion, and the second half the scientific issues.

General Non-Scientific Concerns

Because these are ``meta-issues'', not directly relating to the science of the paper but to the impact of this important journal on society, I would greatly appreciate the inclusion of the GRL editor into this debate. I will gladly accede to the wishes of the editor, but only after he has read my defense.

1) Both referees remarked that the tone is ``sensational''. I do not refute that observation, but I do refute the implication that it is undesirable, at least, in the sense defined by Referee A. I have attempted to use less jargon and a less formal style in the hope that this article will be read by the wider audience of geophysicists who read GRL. If the major concern is about the word ``killer'' applied to this electron population, then I defend that below. If the style is too informal, then I would beg the editor be the arbiter.

2) Referee A would like me to use ``energetic'' or ``outer radiation belt electrons'' to describe ``killer electrons'', viewing the latter as an unscientific definition, and an example of sensationalism. Let me begin this defence by saying that I did not invent this phrase and originally felt the same way about the use of it, but I have slowly come to change my views. Obviously, it can be changed without affecting the science of the paper, but there are good reasons to use such a descriptive adjective:

(a) I would beg the referee to consider such scientific terms as ``whistlers'' or ``lion-roars'', which can be both very graphic as well as scientific. Think carefully over the use of ``radiation'' in ``radiation belts''; sunlight is radiating, but this is not the connotation of this word, rather ``radioactive'' or ``ionizing radiation'' comes to mind, which is precisely why the word has stuck. The question is not whether a newly coined term is ``scientific'', but whether it is necessarily descriptive, e.g., does it fill a void by capturing the essence of a category that otherwise receives ambiguous and inconsistent long descriptors?

(b) Other titles:

``Energetic'' is far too vague an adjective. It means 1 eV to a ionosphere person, 100 eV to a plasmasphere person, 100 keV to a ring current specialist, 100 MeV to SEP person, and so on.

``Outer radiation belt electrons'' is both cumbersome and inaccurate, since it specifies a place rather than an identifier, or more precisely, it makes an identifier appear to be a location, since the outer radiation belt is defined by the presence of MeV electrons (note the circularity of the definition!). What then does one call 10 keV electrons also found in the outer zone? What about low-altitude measurements of electrons made with SAMPEX? What if, as we argue in the paper, these electrons originate outside of the radiation belts, should they change their name as they diffuse into this location? Is there really a difference between ``outer'' and ``inner'' electrons, between a 1 MeV electron found at L=5 and found at L=3? Are there ``outer radiation belt protons'' as well (can one divide the protons into an inner/outer belt)? In my mind, this phrase has led to more confusion concerning the definition of the radiation belts than it has clarified the population it attempts to distinguish.

``MeV electrons'' is more specific, but it still spans 3 decades of energy, when only the lowest decade is meant. Nor is it in SI units, which violates AGU standards. Nor is it easy to pronounce, usually ``em-ee-vee'' is used, with all the cachet of ``eff-tee-ee'' or ``gee-see-em'', which is to say, jargon to the uninitiated. (This raises the question, why are SI units pronounced fully, nPa = ``nano-Pascals'', whereas these non-SI units remain tri-syllabic jargon?)

``Relativistic electrons'' are also awkward, first, because it sets only a lower energy limit, and second, because it emphasizes a property of the population that seems irrelevant to its measurement or societal impact, while connotating some esoteric physics property which is never exploited.

Thus it seems we really do have a problem naming the population we are studying.

(c) In picking a more descriptive name, one should aim for accuracy if not in denotation, at least in connotation. Rather than attempting a purely denotative name (such as auroral kilometric radiation) that rapidly collapses into tri-syllabic jargon, I have chosen to use a descriptor coined, I believe, by Dan Baker, and used by him for at least 3 years at AGU talks for this exact population. The connotation of this word ``killer'' is that the electrons are dangerous to humans and life, and perhaps secondarily, to complicated human machinery. From a non-scientific and societal point of view, this is the most important property of this population and might even be called a defining characteristic. If we have our ``radiation belts'', is it such a long stretch to have the ``killer electrons'' that inhabit it?

3) Referee A mentions that since insurers paid >$100M for Telstar 401, it has an impact on what should be published in the scientific literature. ``With this magnitude of liability, one should be careful about reporting or publishing statements about the Telstar satellite that cannot be supported by evidence.'' Naturally, as scientists, we should always be careful about making statements that cannot be supported by evidence. At the outset, I acknowlege that I should have been more careful when attributing this failure to a DDD, though I do believe there is much evidence in support of this working hypothesis. The fact that the repair of the HST mirror cost NASA in excess of $500M did not hinder scientists from publishing accounts of the error or on speculating on the reasons for such an error, nor should it hinder us from attempting to understand the failure of Telstar 401.

One difference, perhaps, between the HST and Telstar 401, is that NASA is self-insuring whereas private insurers covered the cost of the satellite. Therefore I have called the world's leading insurer of telecommunications satellites, Generali of Trieste, Italy. I spoke with a deputy of Mr. Paolo Albanese, a Mr. Citrone (sp?) in the Space Department, about the impact of scientific research on insurers and the liability I might incur. He said that his company was not directly involved in the Telstar 401 claim, and he expressed surprise that I should incur any liability. He said that he couldn't speak for the American legal situation, but it wasn't common in Europe. He then asked me if I was offering my services to the company and remarked that several universities and private corporations had already contacted them about doing risk assessment for the problem of ``radioactive electrons''(!). He seemed well aware of the space weather implications and seemed to think I had much company in this research.

The conclusions I drew from this phone call, therefore, are that GRL has little to fear about liability in publishing these results, that they are already well known to the insurance companies. If anything, the publication of scientific studies might undercut the market for private risk assessments and reduce their value.

However I did not want the issue of Telstar 401 to cloud the important scientific results observed by POLAR, and have therefore removed it from the paper.

Specific Scientific Questions

Referee A:

0) Referee A argues that we have been guilty of factual inaccuracy in too many places to recount. This is unfortunate, because our desire is to publish a factually correct report. I will address all those mentioned in the referee report, and beg the referee to make a complete list, if possible, available to us. Our e-mail is: r*, and if the GRL editor would forward it, the authorship would remain anonymous.

1,2) Point one is mainly about style, which I have addressed above. The last sentence concerns the Telstar 401, which, as we said above, has been removed from the manuscript. [Note: the orginal response listed the evidence for the Telstar 401, DDD, which amounted to 2 pages. However on consultation with other authors, the decision was made to abandon a "hot button" in favor of getting published. Since the effort was in vain, I list the original text in favor of a Telstar 401 DDD. First Draft of First Reply]

3) The referee does not argue with the claim that we have convincingly shown that the Earth's cusp can trap particles (which alone is surprising enough), in fact, the referee seems to accept it as proven. However the referee takes umbrage with the idea that such a cusp trap can accelerate charged particles, and feels that a numerical calculation should be required (rather than the analytic calculation I used) to prove my assertion.

Whereas I can sympathize with the desire for ``computer'' proof, I think it is neither necessary nor sufficient in this case.

(a) Not necessary, because the Earth already has a well-understood trapping region in which acceleration is occurring continuously, the radiation belts. Knowledge gained from the study of the 3 dipolar adiabatic invariants is directly applicable to the cusp, once we have established that there are 3 cusp invariants of the motion. Models of the radiation belts that ``proved'' the occurrence of acceleration did so without the benefit of computer simulations, using only analytic representations of the fluxes. Once we have established that the cusp has invariants, we can write down the acceleration expected nearly analytically.

(b) Not sufficient, since the observation of the global cusp electric field is in a very rudimentary state (in part due to the semi-random location of the cusp), and would be simulated, more than likely, inaccurately. That is, by giving the modeller free reign over the electric field boundary condition, any acceleration desired could be obtained on any timescale, without necessarily revealing the true nature of the mechanism. As an experimentalist, I grow increasingly skeptical of computer modelling as a means to predict any non-empirical phenomena.

Now that I have vented my distrust of computer modelling, let me address specifically the objections/requests made under this point.

3.1 Insufficient evidence for cusp acceleration?

On the contrary, by showing that the phase space density surrounding this location show less particles without than within, one has direct empirical evidence for {\em in situ} acceleration.

3.2 Insufficient evidence for cusp particles supplying ORBE?

The fact that no alternative theory exists suggests that any theory is acceptable as long as it does not violate physical laws. Indeed, some have seriously suggested Jupiter as the source of MeV electrons, a theory which, unfortunately, did not hold up to scientific scrutiny. Which is to say, the criteria for a valid scientific theory is not certainty, but falsifiability; the ability to be shown false (see Karl Popper's writings). Certainly this theory can be proven false very easily: if the phase space density within the cusp is lower than that in the radiation belts, then ``simple'' diffusion theories would call it a sink rather than a source. We have shown that the count rates are higher in the cusp, in our revised manuscript we show that the phase space densities are higher as well. If another falsifiable characteristic were identified, we would be glad to subject our population to the test, but to claim insufficient evidence is to imply a falsifiability criterion, which we assume are implied in the following statements, and to which we reply below.

3.3 Test particles were traced in a T96 model without electric field?

The implication is that if we had included an electric field, we would not have found trapped particles. This falsifiability criterion can be easily dismissed by drawing on what we know of cusp electric fields. The POLAR/TIDE experiment can measure the cold plasma flows within the cusp. They found, during similar if not exactly the same cusp crossings, a flow primarily in the field aligned direction, i.e., outflows, and only a slight breeze in the transverse direction. My recollection of their findings, reported at the FALL AGU, were that 40 km/s flows were typical, which if we assume a 25 nT field, correspond to about 1 mV/m.

If we assume that this is a global cusp DC field, then from the T96 model that I plot, we have about 30 kV across the cusp. Using a Hamiltonian approach to the description of drift orbits, we know that E-total = K.E. + P.E. = mu Bm + q U, where mu is the first invariant, Bm is the mirroring field strength (<100 nT), q is the charge and U the electrostatic potential described above. Then an increase of 30 kV in potential from one side of the cusp trap to the other will decrease the kinetic energy by 30keV. Since mu is conserved, this means that Bm will have to decrease. Now this decrease cannot occur by changing the pitchangle, since this would change mu as well, thus this only be accomplished by having the drift orbit move toward lower |B|, e.g., by moving cuspward. Since nearly all the energy in these trapped electrons is in the perpendicular component, we can roughly say that a 100 keV electron must move such that a 30\% decline in |B| is effected. If we look at |B| in the cusp, we see that this can be accomplished quite easily, since the cusp goes from 10-100nT over this range of distances and has plenty of dynamic range to account for electric field distortion of the drift orbits. Note that we have now traced trapped orbits up to 1400 keV, which have a proportionately smaller distortion in their drift orbits due to a 30 kV potential.

3.4 The authors claim a large electric field is necessary?

The implication is that the DC electric field of 1 mV/m discussed above is not sufficient to accomplish the acceleration of MeV electrons. We do not claim that these electrons are accelerated by purely adiabatic motion of the sort described in the previous paragraph. Rather we argue for the necessity of resonant scattering and/or AC electric fields, which can transfer energy to the electrons by coupling to the 3 characteristic frequencies of the electrons, the gyration, bounce and drift frequencies. Power at these frequencies is available, and indeed, the EFI experiment on Polar shows broadband electric field fluctuations with RMS exceeding 10 mV/m.

3.5 No quantitative evidence of sufficient energization is presented?

As we argue in point 3.2, lack of evidence implies a falsifiability criterion. It is unclear what that criterion is. Do I need to demonstrate a timescale, or an energy change or something else? Does ``sufficient'' mean that I need to illustrate how a keV electron gains an MeV? If so, we have shown how the limiting case of ``Bohm diffusion'' illustrates exactly this point. If I were to replace Bohm with ``Chorus waves'' would this change the essential argument? If the referee could be more precise, I could answer the criticism more concretely.

3.6 Perform test particle simulation with model electric field?

We are intending to do exactly that. I should point out that the test particle tracing has been computing continuously for 6 months since fall AGU and is now running 1400 keV electrons. It takes 1 day of real time computing to execute 300 seconds of cusp trapping. These simulations are not quickly made. I have no doubt as to the outcome of the simulations, but if this run would convince the referee, I would be eager to run it. That is, I have limited resources of time and computing, so that if the referee made this the \#1 priority, I will run it immediately. The energy, however, will demonstrate purely adiabatic effects unless I include stochastic electric fields. This then runs into the whole question of boundary conditions. If the referee will not fault me for my boundary conditions, I would again be happy to include stochastic electric fields in the simulation. The results will be entirely predictable and inconclusive, however, as I have argued at the very beginning.

4) Arguments are largely conjecture?

It is difficult to separate the denotation from the connotation in this paragraph. All hypotheses are conjecture. Does this invalidate them? No, they wouldn't be hypotheses if they weren't. What would invalidate a conjecture is a testable criterion (falsifiability) that contradicts the predictions of a conjecture. We conjecture that Jan 10 was a fortuitous day for a magnetic cloud to accelerate electrons because it was close to winter solstice, and the cusp was tipped toward the sun. This seems to be both a valid hypothesis and easily falsifiable.

When the referee writes ``Where is the proof?'' I am unclear as to what aspect of the hypothesis he is objecting to. The proof that the cusp is tipped toward the sun lies in solid geometry and knowledge of the Earth's magnetic and spin axes. The proof that acceleration occurred much faster than normal lies in the energy time plots from GEO, HEO and Polar, showing a less than 12 hour acceleration time. This is faster than normal if one uses the SEC MeV electron prediction algorithm developed by Koons and Gorney 1991. It is also faster than normal if one uses the many references (e.g., Baker et al, 1997) to a 24-48 hour time delay in the MeV electrons. The proof that there was a causal relationship between the two is in the conjecture presented, a simple chain of logical relations as follows: a) a cusp that is tipped toward the sun has stronger magnetopause fields b) stronger magnetopause fields lead to a larger volume of phase space that is trapped in the cusp c) A large volume of phase space CAN lead to a more efficient acceleration process d) Electrons that leak out of the cusp may arrive in the radiation belts. e) A more efficient acceleration process CAN lead to a faster rise in the ORBE.

All of these statements are falsifiable. All can be disproved. This then is the ``proof''.

If in our paper we have not clearly outlined the logical steps above, then the fault lies with us for having hidden the details of our conjecture. If, however, the referee is demanding incontrovertible proof of the validity of our theory, then we must object that this is a goal unobtainable in the natural sciences.

5 [1]) SEU?

The inaccuracy is ours. If an SEU is defined to be a heavy ion disruption, as it is typically used in the literature, we should not have applied it to our MeV electrons. We were using it in the sense of a CMOS memory bitflip that can occur because modern chips have shrunk the size of IC chips so much that parts are becoming ``soft'' even to MeV electrons.

6 [2]) Selesnick phase space density profiles decline with increasing L?

I agree with the referee that if the phase space density declines with increasing L, any normal diffusion model would predict a source at low-L. Is this what Selesnick and Blake plot in figure 1 (GRL, vol 24, page 1348)? Note carefully that the first column is differential flux, j, whereas the second column is phase space density f, plotted at constant magnetic moment. Orbit 283, (top panel) indeed shows a source at L=4. Orbit 439, however, shows a source at L>7. Orbit 273, shows an annoying double source, one at L=5 and one L>7.

How do we interpret these results? The abstract is clear: ``Radial profiles of electron intensity and phase space that particle injections followed by fast radial diffusion lead to the main part of the outer radiation belt near L=4 to 5 during active periods. In quiet times the belt is supplied by inward diffusion from an external source. Various combinations of these two basic configurations are also seen.''

To rephrase, when the slope of f indicate a L<7 source, this can be interpreted as the slow decaying remnant of a previous injection. Since the loss or transport rate is faster at L=7 than at L=6, one would expect the decay after an injection to produce a negative slope with increasing L. Note that Selesnick carefully does not say where the radial location of the ``injection'' mechanism is located. It may also be located at large L-shells, and during the first few minutes/hours of an event, send a wave of higher density ORBE radially inward. When this wave is observed after some time, loss processes would disguise its origin. Which is to say, steady state diffusion models cannot describe a non-steady state injection mechanism very well.

Regardless of the injection mechanism, Selesnick is in complete agreement with us concerning the location of the quiet-time source, which is exactly the time period for which the diffusion model is best suited. Contrary to referee A's rebuttal, we find strong confirmation in Selesnick's work for a large L-shell source and additional support can be found in XinLin Li's work published earlier in GRL (vol 24, page 923). Thus I strongly refute the referee's critique, and emphatically reassert that no acceleration mechanism has been found for MeV electrons within the dipolar trapping region itself.

7 [3]) Definition of 'major killer electron' event?

At first I did not understand the difficulty in our nomenclature, but after rereading the referee's comment, I perhaps see the confusion. If we insist on ``killer'' as a descriptive term for these electrons, does this mean that by definition a ``major event'' should cause spacecraft disruption? No, because the spacecraft could be radiation hardened. Nor should the characteristics of the population we are describing depend on the observational technique. ``Killer'' then only refers to the energy of the electrons, not to their effectiveness in any given storm. Then what is the meaning of a ``major killer electron event''? Only that it be the highest recorded flux in comparison to some baseline. I chose April 15-20 because it had the highest recorded MeV flux for all of 1996.

8 [4]) Flux units?

The units have been added to the figures, we apologize for the omission.

Referee B:

1) figures?

We apologize for the print size in Fig 1. We can certainly rectify this with judicious use of a graphics editing package. My version of the plot shows that 01:00UT has an L-shell of 22.7, not 35, so perhaps the print WAS too small. We will specify the fluxes in cts/s-sr-cm2 which can be converted to phase space density if one knew the average energy response of the channel, which turns out to be a ill-defined problem in regions where the spectral index changes rapidly, hence our tendency to only give counts.

We will expend some effort on figure 2, showing it in two perspectives to validate the ``lily orbits'' description.

We have deleted the third figure.

2) Abstract?

We will change the abstract to better emphasize the scientific content of this paper.

3) The discovery of the outer radiation belts was in 1958, giving 1997- 1958 = 39 years. The reference could be made more timely. I have therefore changed it to a 1959 JGR reference.

4) Li reference is updated

5) phase space density is computed and demonstrated in the plot.

6) The trapping in the T96 cusp existed for at least 300 seconds, or for more than 4 complete drift orbits around the cusp. As we state, this is without an electric field, though it is hard to imagine how an 800 keV electron would be detrapped by a 1 mV/m electric field, (as we argue in our reply to Referee A). That is, these electrons appear to be rather permanent residents of the cusp barring topological changes to the magnetic field geometry.

7) We have elaborated on stochastic acceleration. We hope it has answered more questions than it raises.

Robert Sheldon