1 st Year MPhil – PhD Transfer Report

A Model of the Proton Aurora in the Atmospheres of Earth and Jupiter

Philip Stobbart

A Model of Proton and Electron Precipitation

Philip Stobbart

Abstract

The Atmospheric Physics Laboratory, APL, runs a spectrograph in collaborationwith Southampton and Boston Universities. This project was to work towardsproducing a computer program to fit the theory of emission and absorption in theproton aurora to the output of this detector. Also, the various atmospheric modelswithin the department could benefit from parametrizations of runs of this modelunder certain conditions. This report examines the interactions simulated and howthey are developed into a working model, using Fortran 77. The continuingprogress of the model from a 4 th year project to a PhD project is charted, with areview of how future developments predicted in the former project have beenrealised in the current one. The results of the model are presented in the cases ofthe Terrestrial and Jovian atmospheres. The obtained ionization rate profiles arecompared and their uses examined. Finally, a review of present and future work ismade.

1.0 Introduction

1.1 Project BriefThe Atmospheric Physics laboratory has built and runs a spectrograph assembly onthe island of Svalbard in the Arctic Ocean. This is used primarily for research intothe aurora, by looking at the different emissions from the Northern Lights. Thespectrograph is normally used with one of two mosaic filters, covering up to ninelines of interest. The three band filter observes in the H (4861 Å, including the4844- 4876 Å range), N2

+ (4709 Å, first negative bands) and N2+ (4652 Å, first

negative bands) lines. The four band filter observes the Hydrogen beta line andthree oxygen lines; OI (8446 Å), O+ (7327 Å, with range 7280- 7400 Å, whichincludes three OH lines) and O2

+ (5580- 5650 Å). Interpreting these data relies onmodelling work done by collaborators at the University of Southampton andBoston University. They have models that take a particle beam, the energyspectrum, flux and characteristic energy of which has been specified, entering theatmosphere from above, and predicts the emission spectra that would be detectedfrom this. These modelled spectra are then compared to data from thespectrograph and adjusted to try and get a better fit of data to theory. In this way,it is hoped to understand the nature of particle inputs to the ionosphere fromabove. APL would like to be able to get some independence from its collaboratorsand generate at least part of the modelling procedure itself. It would also be usefulto generate parametrisations of this code for use in APL's Global CirculationModels under various conditions.

The program would bring together a number of disciplines including thenature of particle fluxes from the magnetosphere, how particles interact with eachother and an unders tanding of how particle emission lines arise and how theproportioning between different emissions is controlled. The model used bySouthampton and Boston is a very complex, multi - stream model with high timeresolution. This problem can be attacked piecemeal, however, and in tackling theproblem, many processes can be parametrised to get an approximate idea of whatis happening. Over time, these approximations can be replaced with more realisticand complex simulations.1.2 The ICED InteractionsThere are large families of interactions incoming particles can undergo. Theserange from familiar interactions, such as elastic collisions, to more exoticinteractions, such as proton addition leading to nuclear fission. These can be cutdown by looking at the most likely reactions for the energy ranges expected. Forprotons and other heavy ions, there are four main interactions, one of whichrelates to only molecular species. These are Ionization Charge- exchange Excitationand Dissociation, the ICED interactions. The effect of these interactions is to heatthe atmosphere, alter relative number densities of ionic and neutral species and soaffect the overall chemical balance as well as to create light and other observables.

Ionization is the stripping of an electron from an atom, ion or molecule toproduce an ion, an electron and the original ionising particle. Direct ionizationaffects chemical balance in ways that will be discussed later. The products of thisinteraction are high energy ions and electrons that can then go on to furtherinteract with the atmosphere. Protons are more efficient ionizers than electrons,producing more ions at lower energies. This is due to differences in the size, massand charge of electrons and protons affecting how they interact with the orbitalelectrons of the atoms and molecules they interact with. Ionization can involvedtransferring energy to electrons in different shells. This means some ionizationswill require more energy than others, for example, removing an inner shell electron

takes more energy than taking one from the outer shell due to intra- atomic forces.Charge Exchange is the transfer of electrons from one species to another. It

can happen between two multi - electron ions, an ion and a neutral or two neutrals.Only the latter two pairs are considered in the present sets of models as nobackground ionic densities have been put in. This is the most important processfor protons on a number of levels. It creates the majority of ions. It also allowsprotons to become hydrogen atoms, or even negatively charged hydrogen ions. Atthis point, they can begin to emit light independently, rather than having to exciteneutrals. It also allows the protons to leave their flux tubes. Charged particles arebound to lines of electromagnetic flux, about which they rotate with a definedgyro- radius. Neutral particles are unaffected by the field lines and do not rotateabout them. The mass difference between electrons and the positive ions theyrecombine with means the resultant particle will be far slower than the impactingelectron, due to conservation of momentum, making it less likely that it would thengo on to ionise as the free electron would do. By the time the electron is at a highenough energy to produce an ionising resultant particle, the cross - section forrecombination falls dramatically, and the process is no longer favoured. Forprotons, the capture of a small electron from another species doesn't affect itskinetic energy considerably. Energetically, the process is the same as ionisation,except that the emitted electron ends up being captured by the thing that removedit from its shell.

Excitation covers two processes – Kinetic and Electronic excitation. Kineticexcitation is modelled, generally, on the basis of elastic collisions between particles.However, the interactions are more complicated than that. The majority of'collisions' will be the effect of two electromagnetic fields interacting with eachother for a given amount of time, analogous to the tidal effect of the Moon on theEarth's oceans. If the Moon where to orbit faster, or a Moon like object were to passthrough the orbit of the Moon quickly, then the ocean would have less chance toreact to the gravitational forces. This principle helps to understand the change incross - sections with energy, but also indicates the proton can 'hit' or interact withan object and not always be backscattered. The effect of Kinetic excitation is toproduce a large number of fast neutrals that can then go on to interact further withthe atmosphere. Electronic excitation alters the configuration of electrons in theshells of the particle being excited. This can lead to emission as the electrons fallback to their original position. It can also affect chemical balance as some excitedparticles are more likely to interact than their unexcited counterpar ts due toelectrons being available further from the nucleus.

Dissociation is the disruption of molecular bonds by other particles. It leadsto a depletion in molecules and an increase in atomic and ionic species relative tothem. This will have an affect on chemical balance, as well as leaving excitedparticles and having a heating effect. Dissociation requires a two stage process tomodel it. Firstly working out whether or not the interaction occurs, secondly,working out how the molecule splits up as there are often many different ways thevarious parts can be divided up into.

The electron equivalent to the ICED interactions would be the RIDEinteractions. They cannot undergo charge exchange, but instead undergorecombination with far heavier nuclei, leaving behind a fast neutral. There is adifference of about three orders of magnitude between the mass of an electron andthat of a nucleus. In the simplest case, a sixty keV electron hitting a nucleus andaccelerating it would leave behind a thirty electronvolt neutral. Although thisenergy would allow further interactions to happen, the chances of such a highenergy electron recombining are low. The cross - sections for electron interactions

are highly sensitive to energy in comparison to those of the proton. Cross - sectionsfor any given energy and interaction with a given particle are also often lower forelectrons than protons. This means the probability of interaction with a givenmedium is both always lower and always changing faster with energy for electronsthan for protons.

2.0 Fourth Year Project

This program began as a simpler 4 th year project during my undergraduate degree.The literature review undertaken in this project set out the main theory behind thecurrent project. The outcome was a small program that was able to predict theratios of secondaries created by the primary beam at each altitude, as well as someanalysis of what happens next, which still underpins the main parts of theprogram. The structure of the simple program – datasets of atmospheric densitiesfrom MSIS and interaction cross - sections read into a program that then works outa probability density function and uses a random number generator to decide whathappens in each run – is identical to the basic structure of the later program. Theproject can be split into four main sections. The proton beam – describing theinput into the program. The atmosphere – describing the background neutraldensities and temperatures. Cross - sections – combining the first two aspects of theprogram into a probability density function. Products – a look forward to thefuture of the simple model.2.1 The Proton BeamThe incoming protons in the solar wind start their journey in one of two streamsfrom the Sun. The fast and slow streams are both channelled into the Earth'smagnetosphere through reconnection of the Earth's magnetic field with the solarwind's frozen in magnetic field. They are accelerated through processes in theEarth's magnetotail, reaching high kinetic energies, and then are transported to thepolar region, where they interact with the ambient species to form the aurora.

The channelling and production methods collimate the energy, leaving whatis believed to be Maxwellian distributions in energy about certain characteristicenergies. In Galand et al (1999) the ionisation rates of three Maxwelliandistributions are compared and this type of general energy distribution is preferredwhen modelling auroral protons. For a simple model, however, it is easier tosimulate the effect of a monoenergetic beam of particles impacting on theatmosphere. The decision on which energy to chose was a compromise between theenergies at which protons are believed to precipitate and those for which cross -sections were readily available. 5 keV was close enough to an average energy to bereasonable, and has a number of available cross - sections.

By the time the protons have descended to the altitude at which they startsignificantly ionising, magnetic and electric effects on their path are reducedenough for them to be modelled as falling straight down (Galand et al 1999 andreferences therein). As the effects of the pitch angle determined helical pathhaven't been include, the protons' energy represents the field aligned component oftheir total energy. For relating this to the total energy, a simple trigonometricrelation between the two energies is that the field aligned energy is the cosine ofthe pitch angle multiplied by the total energy. This takes into account mirror pointsat which the pitch angle rises above ninety degrees and reverses the direction ofthe proton. Although a simplification, this does mean the energy spectrum and thepitch angle spectrum would have to both be considered when comparing theresults of the model to other data.

2.2 AtmosphereThe model's two potential uses as a research tool for Svalbard and the possible usewith other models meant it made sense to allow a modular atmosphere. Whilst anatmosphere could be designed and included in the model itself, that atmospherecould then be slotted out and another one put in so that, for example, the modelcould be used with the Jovian GCM JIM as well as the Terrestrial models and othersthat APL develops.

For an initial atmosphere, MSIS- 86 was run. The Mass Spectrometer andIncoherent Scatter model includes a large amount of data from satellites, radarsand rocket campaigns. Spherical Harmonics are then used to fit a full atmosphericprofile of the densities of H, He, N, N2, O, O2 and Ar as well as thermospherictemperatures from 80 – 800km altitude. Variations in composition due to seasonal,diurnal and solar - magnetic changes are accounted for. The co- ordinates of aspecific point of the Earth are inputs, allowing for latitudinal as well as longitudinalchanges.

The general idea of using an entirely self contained atmospheric model wasthat the model could read its output into an external file. The auroral model wouldthen use this output as its background atmosphere and perform its interactions onit, reading out its output into another file. This output would then be put back intothe model atmosphere, recalculated and passed back into the auroral model forfurther calculations until either a self consistent answer emerged or interim effectscreated by more diffuse aurora were replicated.

The program was not expected to be well developed enough to read outresults during this project, and limitations on the time allowed for each run meantthat this plan was changed. The output of one MSIS run was placed in a commonblock for use with all runs. This compromise allowed the program to run withouthaving to call MSIS, by far the most computer intensive part of the program, whilststill allowing the outside atmospheric program to remain separate from the auroralprogram.2.3 Cross - SectionsThe final piece of the puzzle as far as the external datasets were concerned was thecross - sections. These are the glue that allow the atmosphere and the interactionsto come together. Each cross - section, between particle A and particle B, say, givesthe probability of particle A interacting with particle B. This probability isnormalised so that it becomes the area of a disc centred on particle B that particleA will see before it. To find the probability of A undergoing the interaction with Bat any given altitude step, multiply the number of particle B in the volume beingconsidered by the cross - section for the interaction and the length of the volume ,before dividing by that volume. This simple equation underpins both the 4 th yearproject program and the current program.

When a number of different particle Bs are being considered, a number ofdifferent cross - sections are used to give a corresponding number of probabilities.These are summed together consecutively to give a probability distributionfunction. The excess probability represents the chance of the particle passingthrough the volume with no interactions occurring at all. This can be a simple caseof taking the cross - section of a particle hitting and doing something to anotherparticle for each species considered. It can also be made more complex by takingthe cross - sections for each interaction being considered individually for eachspecies. It can further be made more complex by not considering absolute cross -sections (based on the probability of interaction) and differential cross - sections,based on the probability of an interaction leading to the incoming particle beingscattered by a certain angle. Absolute cross - sections are obtained by integrating

the differential cross - section over two pi radians.Cross - sections are energy dependant. They begin at a certain activation

energy and rise as the incoming particles gain energy, which they can use to moreefficiently interact. At a certain energy, the particles start to become too fast forthe tidal disruption described earlier. The cross - section falls at this point,eventually following the 'hard' cross - section – when the central particlesthemselves are hit – asymptotically. This change is far more severe for electronsthan protons and the heavy ions. In addition to this energy curve, there are certainresonance points. This occur, for example, when incoming particles of certainenergies are able to excite electrons in certain energy levels. These are veryimportant in dissociation, when the electron positioning is vital to the strength ofthe bond, and in ionisation and charge exchange, where electrons can by ejected orstripped more easily at certain energies than others. The study of these resonancesand of cross - sections in general is very complex and very incomplete. The searchfor even the simplest collisional cross - sections continues to take up a lot of time.Of some help was the database of Rice University. Internet and literature searcheshave shown that other databases have been set up, but these are either lesscomplete or concentrate on species not present in the MSIS atmosphere. Of specificconcern are collisions between oxygen atoms, and those between oxygen molecules.Both are important interactions, but very hard to replicate. Even when cross -sections have been found, getting them at the right energies is difficult. The 4 th yearprogram used the absolute cross - sections of the individual ICED interactions ofeach of the MSIS – 86 elements at 5keV or a close energy, with the proton theincoming particle in each case. This worked out at twenty - three cross - sections.2.4 ProductsOnce the PDF has been worked out, using the cross - sections, the final part of theprogram is to use a random number generator to choose between the variousprobabilities. In this case, the intrinsic Random Number Generator of Fortran wasinvoked. This provides a pseudo random string of numbers between zero and one,with a linear probability distribution function. When an interaction is chosen, it wasreadout along with the particle that interacted and the likely products.

The main results of the 4 th Year Project concerned the initial interactions andthe products, secondary particles, expected to result from them. The rise inprobability of interaction and the ratios of numbers of interactions with eachparticle as well as ratios of expected secondaries were produced. To go with this,calculations of the expected energies of these products were discussed. The reasonfor this discussion was preparation for the next stage of the model. Havingproduced these new species, it would be important to track their progress in thesame way as protons had been tracked. The ratios of particles interacting withparticles gave an indication of how cross - sections and densities come together toproduce a likelihood of interaction.

The final sections of the project dealt with speculative suggestions for futurework. Some suggestions were simply following the logical course of action andexpanding the model to continue along its present course of action and precipitatethe secondary particles, as well as feeding back into the atmosphere. The othersuggestions centred around expanding the program to other uses. Firstly extendingthe primary particles from simply being protons with a set energy, precipitating at600km to any particle of any energy at any altitude. Also suggested was trying outother atmospheres and making the various energy concerns more complex andrealistic; extending the monochromatic energy spectrum to Gaussian or Maxwellian,for example. These aims have set the tone for the later project. Some, like the usein other atmospheres and the precipitation of other particles as both primaries and

secondaries have been achieved. Others, like the extension of the energy spectrumare still being worked on, but are now more than just speculation.

3.0 The MPhil /PhD Project

After a year long hiatus, the program was revived as an MPhil/PhD project . Thefourth year project had proven the feasibility of at least attempting to create aprogram of this sort. Although the original program had been lost in the theft of alaptop, and the backup lost when UCL deleted my original userid, there was enoughinformation to recreate the simple structure of the program in my fourth yearreport. The recreation and running of the new version of the original model wasaffected by the lack of computers for new students in the first few months of theproject. The computers that were available were pretty slow. Completing studentswere running highly intensive models on the faster computers. Although there wasan introduction to internal computing, little was known of other computersavailable that were intermediate between the Alphas and the G4s. After threemonths, new computers and a second fast computer began to arrive and theproject began to take off quite rapidly. Model runs were suddenly an order ofmagnitude faster.

The initial work on the program was to increase the number of particles itcould precipitate. The secondaries and higher order products were followed fromcreation to thermalisation. Next, the interactions themselves had new subprogramscreated to simulate them. Then electrons were put in as potential primary particles.The program was tidied up quite a bit, the atmospheres exported to external filesand the Jovian atmosphere plugged in.3.1 Following the SecondariesThe creation and thermalisation of secondaries was the first concern in extendingthe program. When a proton interacts through any of the ICED interactions, or anelectron through the RIDE interactions, they leave behind some sort of a product.This may be fast neutrals or ions or electrons. These will then be able to go oninteracting as the protons and electrons do. With each interaction, the incomingparticle will lose energy. At some point, the energy will fall to the level at which it isequal to the thermal energy of the gas it is in. The particle is then indistinguishablefrom the gas and the program ceases tracking it. It is said to be thermalised. Ionsthermalise at the ionic temperature, which is always above or equal to the neutraltemperature and electrons thermalise at the electron temperature, which is alwaysat or above the ionic temperature. There is currently no ionospheric model in thecurrent model, so all particles thermalise at the same temperature.

To include secondary and higher order interactions in the model, secondary-secondary cross - sections have to be found. Not only do they have to be found, butthey are required over a large range of energies and charges. If they are notavailable – for example O- O scattering – they have to be manufactured – byhalving the O–O2 scattering cross - section. This isn't a very satisfactory situation,but will produce a workable answer until a cross - section can be found. Thisproblem is made worse by charge changing and ionisation events meaning thecross - sections between ions as well as atoms have to be found over a wide range ofenergies too.

Protons are more efficient at producing secondary particles at ionisingenergies. It will be a key test of the program whether or not its PDF and kineticstructure can replicate this.

The subroutine created to model the further interaction of the secondarieswas named Strike . It works in the same way as Proton , the main primary program,

except it is more flexible. The seven MSIS species were each given a species ID inthe original program, with protons having their own separate ID. A database ofcharges and masses for each species and a cross - section array that used the ID asan input allowed any of the species to pass through and interact with the MSISatmosphere.3.2 Modelling the InteractionsStrike , in itself, isn't enough to produce a realistic simulation of particleinteractions. It models only the effects of elastic collisions. New subroutines wererequired to simulate the ICED interactions themselves. New information about eachspecies was also required for the interactions to take place. A new database wasformed in a common block. This time, it contained information on particlecharacteristics such as the various ionisation and dissociation potentials, allconverted to electron volts.

The ICED interactions were each considered in terms of what they physicallymeant . Ionisation and Dissociation, for example, both mean the breaking of anelectrostatic bond. In one case, an electron is freed. In the other case, an entireatom or ion is released. They are both activated with a defined potential in thedatabase of the program. They both leave the incoming particle untouched. Asingle subroutine, Break , was created to deal with both of them. This has databasesincluded on both the molecules and the probabilities of them breaking in certainways. Their branching ratios were worked out by taking ratios of the cross - sectionsfor production of certain ions and atoms. In the case of ionisation, the charge ofthe ionised ion was simply incremented by one and an electron ejected. In bothcases, energy is redistributed in a two stage process. Firstly between the incomingparticle and the particle to be ionised or dissociated, then between the differentparts of the ionised or dissociated particle.

Excitation, in the kinetic sense, was still dealt with through Strike . A functioncalled Energy was created which uses conservation of momentum laws toredistribute the energies of colliding particles. No function or subroutine forelectronic excitation yet exists for this program.

Charge- exchange has two methods, both dealt with in the subroutine Swap .These are neutral - neutral and ion- neutral charge exchange. With there being noionosphere in the model, there is no ion- ion interaction yet. Both of these requireelectrons leaving one species and attaching themselves to another. This requiresthe ionisation potentials, the ability to change the charge of the primary particleand a PDF to decide which species loses and which gains the electron.

This meant the first major change in the program. Up until then, the primaryparticle precipitation had been the main part of the program, with the protontreated separately from the other particles. Now, protons looked as if they wouldno longer remain protons, as they had previously done, when travelling through theatmosphere. Charge exchange events would create hydrogen from them, eventaking the process as far as the negative hydrogen ion, as well as returning them tobeing protons in a constantly changing proton / hydrogen beam. The section thatran the protons looked like a simplified version of Strike . It was excised and putinto a separate subroutine of its own. The main program was left to read in theatmosphere and the energies and set up the common blocks before calling this newsubroutine. The proton ID number was removed and protons listed as hydrogenwith a charge of +1. The charge of a particle became a new variable, and it was atthis point that the cross - section array expanded to include new charges.

Runs of the improved model showed all the ICED interactions werehappening and doing what they were supposed to, at least to the first order.Ionisation produced electrons. Elastic collisions created fast neutrals. Dissociation

broke up molecules and charge exchange allowed H, H+ and, for brief periods, H- tobe seen. The ionisation potential of H- is less than zero and it tends to last only fora few kilometres, whereas H and H+ can go on for tens of km before charge-exchanging. The increased numbers of interactions meant that the results files –which recorded what was hit and how it interacted, as well as the energy loss of theprimary, and whether or not an ionisation occurred at a given altitude, became verylarge.3.3 New PrimariesAlthough the primary concern of the model was proton precipitation, it becameclear that other precipitating particles could be modelled in the same way.Electrons are the obvious example, and two other commonly seen particles areOxygen atoms and ions and Helium nuclei. Both are heavy ions and would interactmuch as a proton does. Both have cross - sections already in the model as they areboth MSIS elements. Both have astrophysical uses beyond the remit of the currentinvestigation.

To add in electrons, new cross - sections were sought and characteristics ofthe electron added to the databases. The electron differs from the proton in anumber of different ways – far more than the other two potential primaries do.They alter their cross - sections with energy far more. They have far less mass. Theyhave a single defined charge which will not exchange. But they do recombine –effectively charge exchange without a second nuclei being present. A thirdinteraction subroutine, Rec , was therefore created to deal with this. It simply addedelectrons to positive ions, incremented their charge and redistributed energiesaccordingly. As there is no ionosphere in the program yet, this subroutine isn't inuse. To test the subroutine, the input files were rewritten to replace all N2 in theMSIS atmosphere with N2

+ . The electrons successfully recombined with thismolecule. A future use for Rec could be to deal with photon absorption in themodel, a similar process to recombination.

Once recombination has been taken into account, electrons work, in theory,in the same way as protons do. In this model, the electrons do not work as well asthey could. The changing cross - sections with energy are too dramatically alteredfor the model to currently cope with them. On top of this, there is a severe problemwith the code that will be discussed in the next section. But there are hopeful signsin the interactions that do happen and I am confident that the code will soon beoperational.

It will also soon be possible to use photons in the model. These undergospecific interactions at specified energies and would be fairly easy to track. Theywill be required in the model in any case as they will be the emission that theaurora puts out. Their cross - section sets will be used as their flux will be altered bythe surrounding at mosphere, and the heating effect from this will be important tochemical balance in the model.3.4 Tidying up the CodeThe initial pro gram was a single file of code. This is an inefficient structure to usewhen individual subroutines need to be found and altered, and when it wasintended that new atmospheres could be added to the model. As a result, thevarious subroutines were exported to different modules and initialised with a makefile. The make file contains the names of all the modules in the program andcompiles each one into a binary file. If a version of a source file is found to benewer than that of a binary file, it is recompiled individually. After a binary codehas been compiled, the entire complement of binary codes are added together intothe main program, ready for execution. The makefile also contains all the flags thata compiler might need to properly compile the code.

Changes between compilers have proven very difficult. Code that runs on thef77 compiler on Ball need subtle, but distinct changes for running on xlf onRimmer. Further changes need to be made for other compilers, such as that on thePSE. One main problem is the Random Number Generator. This seems to be a semi-intrinsic function. It was added in later than other intrinsic functions and hasvariations in how it is called. Some compilers require a single starting seed, somerequire different ones, some require that there be none at all. As there is often noguide on how to change the flags to replicate how a previously used compiler hadworked when one starts to use a different compiler on another machine, it can betime consuming to root out problems within the code and makefile.

Another change that was made in the code – and mentioned above – is thatthe primary version of Strike was made into a subroutine. It was then copied andpasted to create the electron primary beam. At the same time, the entire code wasmade more flexible, so each species was effectively equivalent, whereas previously,protons were in a separate category of primary and all other secondary. Theadditions of charges meant the cross - section arrays expanded to include ioniccross - sections. The demotion of protons to H+ meant that a character array thatheld the names of each particle and a further one that held charges could becreated to handle all species.

The final one of the major changes to the structure was the atmosphere wastaken out of the common block and put into external files. In order to make thecode run faster, the atmosphere was read in to the main program only, rather thanin Proton , Elect or Strike , the proton, electron and secondary PDF calculators,respectively.

There were changes to the way some things were calculated. The energyredistribution function was found to be considering equations relating to velocitiesinstead of energies. This was updated. Also a second stream of particles was put in.This used a subroutine called Recoil , which was effectively Strike but trackingparticles moving up, rather than down, the altitude range. As it happens, the earlierrecoding to make Strike more universal so any particle can be precipitated down italso made it very easy to turn it into a routine operating in the opposite directionto its current one. Strike works out its PDF at the altitude it is at, and the only thingcontrolling the altitude is the main do loop. Alterations to the direction the do loopmoved in – from 600- 1 (km altitude) or from 1- 600 – altered the direction theparticles were moving in.

Backscattering, where particles bounce back after an interaction, wasincluded by having half the interacting particles reversing where appropriate. It wasthen ensured that the same code was used in the new subroutine so they couldbounce back again when in Recoil . This, and previous kinetic considerations, allowsthe model to simulate the component of the primary beam's energy parallel to theflux tube it is going down. Careful tuning of the incoming particles' total energyflux and their pitch angle can therefore be used to make comparisons with data.

There is still a lot of work to do on the structure of the program. Thesubroutines Elect and Proton should be able to be absorbed into Strike , as shouldRecoil. A start has been made with putting Proton into Strike and Recoil by havingthe backscattered component of the primary beam go into those subroutines, witha new variable identifying them as primary particles. The code also remains onedimensional, and it will be helpful to have the other two dimensions included. Thehelical path of the protons has an effect on the effective path length. It is alsounfortunate that some protons may be thermalised in the vertical dimension whilststill being very energetic in the perpendicular plane. On top of this, there is theeffect the protons have on the velocity distribution of the gas they're in. They bring

a large vertical component of momentum as well as, via their helical motion,momentum in the perpendicular plane, though this is a second order effect.3.5 The Jovian AtmosphereTo test whether the original aim of a plug and play atmosphere had been achieved,a copy of the model was updated to work with a set of atmospheric densities fromthe Jovian Ionosphere - Magnetosphere model, JIM, Developed here at APL. Thisatmosphere contains H, H2 and He, requiring one new species ID for diatomichydrogen. For later use, another species ID was created for triatomic hydrogen.

The densities of these species were put into their own files, whilst thedensities of all other elements were set to zero arrays. The temperature structurewas also swapped over for the Jovian version. The number of altitude levels waschanged from 600 for Earth to 1979 for Jupiter. On Earth, MSIS - 00 had appearedand extended the altitude range from 0 - 600 km. On Jupiter, information wasavailable from 356- 2335 km. Once these changes were made, the Jovianatmosphere seemed to work well with the rest of the code when protons were putin. When electrons were put in, things were different. If they strike diatomichydrogen or helium, then the code reacts as it should. If they hit atomic hydrogen,then the code will act as if oxygen has been hit. The sudden presence of oxygenprecipitating down with the electrons invalidates any results that come out andraise questions about the code used. A run was attempted with a small amount ofoxygen present. It caused an instant crash of the model, with very little informationavailable from the debugger.

It was recently discovered that the Random Number Generator wasproducing zeros. The PDF is created by looking at the probability of the primaryundergoing interactions with each species in turn. The first thing the model looksat is the probability of elastic scattering off oxygen atoms, which in Jupiter has aprobability of zero. When examining the PDF to determine what happens, themodel looks at each species in turn to see if the Random Number Generator hasproduced a number less than or equal to the probability of interaction. In theoriginal compiler, the Random Number Generator didn't produce zeros, but laterRandom Number Generators appear to do so. The problem was remedied by thefirst set of probabilities having a requirement of the Random Number Generatorbeing 'less than' rather than less than or equal to the probability of interaction. Thisunder reports the probability of the elastic scattering interactions and over- reportsthose of the next interaction by an amount equal to the resolution of the RandomNumber Generator. This is negligible compared to the large errors associated withthe MSIS atmosphere and cross - sections which form the PDF.

4.0 Results

The model was set to record altitudes at which ionisation events – such as directionisation and charge exchange – happened. This direct ionisation rate is a goodpoint at which to compare the model I have created to other models. The emissionsproduced by many models are directly proportional to the ionisation rates ofspecies. In some cases, a defined spectra is simply made brighter by total ionisationbeing high. This would be used, for example, as a way of identifying lines brightenough to be identified under certain conditions. More sophisticated models havespectra linked directly to the ionisation rates of specific species. My model willeventually produce its own spectra using excited states and decay rates. But fornow, it produces ionisation rates that can be compared to other models and be aninput into chemical models that will then produce production rates of entirely newspecies.

A quick note on the results presented here. The Earth and Jupiter modelshave their own quirks and balance of good and bad points. For example, the use ofthree as opposed to seven background density profiles means that the Jovianmodel runs a lot faster than the Earth model. However, the Earth model has 600rather than 1979 levels and so requires less protons to be fired through it toproduce a smooth profile. In each case, I have tried to replicate a one erg cm - 2 s - 1

flux. This is equivalent to Galand et al (1999) in which the total ionisation rate of a5keV beam of protons, as well as a 1keV and a 15keV beam is shown for the E-region of another run of the MSIS atmosphere. This amounts to about 125,000protons, more than enough for a smooth Earth profile, but not quite at the rightlevel for a smooth Jovian profile.4.1 EarthFigure one shows the primary ionisation rate for a one thousand proton run. Thestatistical variance of the rate is very noticeable, but it does show that a peak in therate exists somewhere near the bottom of the E- region, where expected.Figure two shows the secondary beam from the same run. The secondaries arenumerous enough to form a smooth profile. If anything, they are too numerous.Inelastic processes such as electronic excitation would normally remove a lot ofenergy from the secondary beam. Effectively, all the energy that will in the futurebe released as auroral emissions is currently held in the secondary beam and this isexpressed by the size of the peak ionisation rate.Figure three shows both the primary and secondary beams of a ten thousandproton run. There is an unusual kink in the peak of the rate. This may be anartefact of the one stream model and a run of the two stream model wasundertaken to determine this. The primary peak appears to be at around 135 kmaltitude, and the secondary peak at 124 km.Figure four shows the same information, but on a logarithmic scale to facilitatecomparisons with other models. This scale also brings out the primary profilebetter. There is still a bit of variance at this level. The primary beam in these casesis pink, secondary yellow and the sum of the two black.Figure Five is a plot from Galand et al (1999). This shows the profiles of threeenergies of protons, 1keV, 5keV and 15keV. This is used to compare with my 5keVresults. The solid lines represent the main transport model, the dotted lines aparametrisation. The primary beam of my Earth model seems to follow the shapeof the 1keV profile quite closely, whereas the secondary beam is closer to the 5keVshape, with a large excess of flux in the lower ten kilometres.Figure six has been plotted for comparison with figure five. The primary beam ofthe one thousand proton run has been multiplied by a factor of 125 to simulate thesame flux as the Galand plot.Figure seven shows a breakdown of the ionisation rates previously shown for a1000 proton primary beam. All solid lines represent the sum of ionisation rates byH and H+ . Dotted lines represent ionisations by H, dashed represents those by H+ .Yellow diamonds represent the ionisation of N2. Pink X's represent the ionisation ofO. Blue crosses represent the ionisation of O2. The length of the run is not quitelong enough to make this a meaningful graph yet.Figure eight is the version of figure seven from Galand et al (1999). Here, solid linesrepresent the transport code, dashed lines the parametrisation. Triangles representionisation of N2 by H+ . Diamonds are N2 by H. Crosses are O2 by H+ . The stars are O2

by H. The circles are O from both H and H+ . H- reactions were not considered.Figure Nine is the first run of the model with the secondary and higher orderproducts made two stream. The kink noticed in the one stream model has vanishedand been replaced with an even stranger shaped peak. The suggestion is the

primaries peak close enough to where the secondaries are most likely to interact toform a fountain effect, with secondaries interacting in two profiles positionedeither side of the primary beam. Other notable effects are the redistribution of theionisation rate and the movement of the terminus further up the altitude range.The redistribution reduces the peak size and adds to the ionisation rate recordedat all altitudes above the peak.Figure Ten shows a ten thousand proton run with both the primaries andsecondaries made two stream. The peak size has now reduced to the level at whichGaland et al suggest it should be. There is a massive separation between theprimary and secondary peaks, with the secondary peak staying at around 135 km ,but the primary peak now at 300 km. The reduction in the size of the peak meansthe graph shows the statistical variance again. Larger runs are required to removethis, as on Jupiter.4.2 JupiterFigure eleven is the primary ionisation rate from the Jovian atmosphere after a tenthousand proton run. Although Jupiter runs faster for a given number of protons,it takes more protons to produce a smooth run. This also shows that thesignificant ionisation rate begins right at the top of the altitude range. The slowlychanging density of JIM means the change in ionisation rate about the peak isslower per kilometre than on Earth.Figure twelve shows that even after 125,000 protons, the curve hasn't yet smoothedin the JIM atmosphere. It also shows the initial ionisation rate is about half thepeak rate. The curve also has a very noticeable dip at about 2100 km. This turnedout to be a mistake in one of the density files.Figure thirteen shows one of the initial attempts at making the Jupiter model twostream. A lot of flux has been lost in the secondary peak – far too much as ithappens. A bug had developed in the file that records the secondary ionisations,and it had deleted some earlier results.Figure fourteen was a more successful 125,000 proton run with the two streammodel. The secondary peak remains where it was in the one stream model, as doesthe primary. The primaries are still one stream and their profile is unaffected. Thearea of the secondary curve is similar to the one stream version, but the peak hasbroadened upwards.Figure fifteen shows an emission profile from Melin et al (2003). It creates emissionby assuming it is relative to the ionisation rate, and so can provide a quantitativecomparison to the shape of my own peaks. It has a double peak, separated by800km, in comparison to mine, separated by 700 km. It should be noted that thepeaks occur in different altitude ranges of a different JIM run, and concernelectrons rather than protons of unknown energy.Figure sixteen show s the profiles of protons and photons in human flesh, createdfrom research at the Paul Scherrer Institute Proton Therapy section. It shows aneffect that I will be trying to replicate later on. Changing the energy of the protonschanges the altitude at which they interact. The reason can be seen in the photonline above. The rise to the peak is proportional to the inverse cumulativeprobability density function. The fall from the peak is proportional to how manyphotons remain to ionise. Photons are easy to do this for as they interact once andvanish. Protons change energy and therefore cross - section and each protonproduces a cascade of secondaries, but the general idea is the same. The length ofthe rise is proportional to the probability of interaction, and as this is in turnproportional to cross - section for a given density profile, the altitude of the peakhas to be proportional to cross - section and hence energy.

Conclusions and Further Work

Current work concentrates on extending the runs I already have to produce smoothprofiles and finish the two stream coding. Problems do need to be ironed out, mostnotably in the file structure. The old Earth code was transferred to the PSE forlonger runs, but the compiler didn't like recording from multiple recursivesubroutines into the secondaries file. The new two stream model on Rimmer atAPL had a similar problem. The compiler on Rimmer didn't like putting resultsfrom different subroutines into the primary ionisation file. Neither has a problemwith both files in the pair, but they cannot agree which file is at fault.

The code should be extended to include further and more realistic physics.Areas in which single energies are used – such as the resultant energies ofinteractions or the monochromatic primary particle input energy – should beconverted to distributions. The cross - section routine should be rebuilt at a higherresolution to cope with the more dynamic electron cross - sections. Once all this hasbeen done in one dimension, the same ideas and routines should be applied to allthree dimensions. Effects such as the interaction between the two streams up anddown the field lines should also be included. Finally, the results should beparametrised for use in the various General Circulation Models in use at APL toprovide a tool for examining precipitation of particles in as many situations aspossible.

The results from both Earth and Jupiter show that a single framework modellike this can be applied to multiple atmospheres with equally valid results. TheJovian model is faster for a given number of protons, the Earth model is faster tocome to a smooth profile. Earth shows a definite peak separation, but nothing incomparison to that of Jupiter. Other models in use at APL that could benefit fromsimilar analyses would include the Saturn and Martian models. APL also hasmodels of other atmospheres in development, each of which could be applied togive an idea of how precipitation works in different media.

The two stream models led to a lessening of total ionisations, and aredistribution upwards in ionisations in both the case of Earth and that of Jupiter.In the Jovian atmosphere this does not affect the position of either of the peaks orthe terminus. On Earth, the terminus and secondary peak are shifted slightlyupward and the primary peak far upwards. Residual ionisation from the upstreamparticles lost from the atmosphere would be interesting to investigate further. Thefountain effect seen in the partial two stream model for Earth could still beoperating, creating a large backward flow of particles. This flow could beinvestigated by extending the atmosphere used upwards and seeing if theionisation rate remains a background effect or whether or not it rises or dies away.

Data from Doppler shifts of protons in the aurora could be used as a casestudy of the kinetics of the model compared to the kinetics of real particles.Further data that could be used in conjunction with the model include lines such asthose mentioned in section three of Galand et al (2002). H Ly, H Ly, OI, OI,NII andN2 are bright lines in the aurora from short lifetime excited states that require noionospheric model to simulate. They are effectively equivalent to the ionisation rateof the model. Satellites such as STP- 78 have left a legacy of observations of theselines, which could be used to compare with the model. STP- 78 is especially usefulas its orbit was at 600 km, the top of the atmosphere used in the model to date.

The model is ready for testing on further atmospheres and for data to beused in conjunction with other models to validate it. Further work is needed torefine the code to produce a more realistic result and to produce parametrisationsfor the other APL GCMs.

Figure 1

1000 proton run in the MSIS – 00 atmosphere, one stream Primary beam

Figure 2

1000 proton run in the MSIS – 00 atmosphere, one stream secondary beam

Figure 3

10,000 proton run in the MSIS – 00 atmosphere, one stream, both beam s

Figure 4

As above, but on a logarithmic scale

Figure 5

Shapes of some ionisation profiles for comparison from Galand et al (1999)

Figure 6

125,000 proton run manufactured from 1000 proton run

Figure 7

As above, but also separated into some component ionisation rates

Figure 8

Similar to above, from Galand et al. (1999)

Figure 9

10,000 proton run in the MSIS- 00 atmosphere, one stream primaries, twostream secondaries

Figure 10

10,000 protons in the MSIS- 00 atmosphere, fully two stream

Figure 11

10,000 proton run in the JIM atmosphere, one stream Primary beam

Figure 12

125,000 proton run in the JIM atmosphere, one stream Primary beam

Figure 13

Initial Two stream attempt

Figure 14

More successful 125,000 proton run, in JIM atmosphere, with two streamsecondaries

Figure 15

Emission rates in the Jovian atmosphere, from Melin et al (2003)

Figure 16

Comparisons of proton ionisation rates at different energies and of theequivalent for Photons

From the PSI Proton Therapy Information web page. The peak here is knownas a Bragg peak and SOBP stands for Shift Of the Bragg Peak, with the bluelines indicating how the peak moves with changing input energy.

References

“Differential scattering cross sections for collisions of 0.5, 1.5 and 5.0 keV heliumatoms with He, H2, N2 and O2”J.H. Newman et al. J. Geophys. Res. 90, 11045 (1985)“Differential cross sections for scattering of 0.5, 1.5 and 5.0 keV hydrogen atoms byHe, H2, N2 and O2”J.H. Newman et al. J. Geophys. Res. 91 8947 (1986)“Absolute differential cross sections for very- small- angle elastic scattering in He +He collisions at keV energies”D.E. Nitz et al. Phys. Rev. A 35, 4541 (1987)“Absolute differential cross sections for small- angle He+- He elastic and chargetransfer scattering at KeV energies”R. S. Gao et al Phys. Rev. A 38, 2789 (1988)“Absolute differential cross sections for very- small- angle scattering of keV H and Heatoms by H2 and N2”L.K. Johnson, et al. Phys. Rev. A 38, 2794 (1988)“Collisions of keV- energy H atoms with the rare gases: Absolute differential crosssections at small angles”R.S. Gao et al. Phys. Rev. A 40 4914 (1989)“Direct and charge- transfer scattering of KeV energy H+ and He+ projectiles fromrare- gas atoms to obtain small angle absolute differential cross- sections”L. K. Johnson et al. Phys. Rev. A 40, 4920 (1989)“Collisions of kilo- electron- volt H+ and He+ with molecules at small angles: Absolutedifferential cross- sections for charge transfer”R. S. Gao et al. Phys. Rev. A 41, 5929 (1990)“f- electron Rydberg series of triatomic hydrogen”L. J. Lembo, M. C. Bordas, H. Helm, Physical Review A, Vol. 42, No. 11, p6660 (Dec.1990)“Collisions between H+ and H2 at kilo- electron- volt energies: Absolute differentialcross sections for small- angle direct, single and double- charge transfer scattering”R.S. Gao et al. Phys. Rev. A 44, 5599 (1991)“Absolute differential cross sections for electron capture and loss by kilo- electron-volt hydrogen atoms”G. J. Smith et al. Phys. Rev. A 44 5647 (1991)“Densities and Vibrational Distribution of H3

+ in the Jovian Auroral Ionosphere”Y.H. Kim, J.L. Fox and H.S. Porter , J. Geophys. Res. Vol 97, No. E4, 6093- 6101,Apriul 25 th 1992“Excitation of the Lyman- Birge- Hopfield bands by proton precipitation”Z.V. Dashkevich, B.V. Kozelov and V.E. Ivanov, Geomagnetism and Aeronomy,Vol.34, No. 5, (April 1995) (English Translation)“Calculation of Hβ emission in aurora: Comparisons with observations”B.V. Kozelov, Geomagnetism and Aeronomy, Vol. 34, No. 5, (April 1995) (EnglishTranslation)“Simplified algorithm for precise calculation of spatial distributions in combinedelectron- proton- hydrogen atom aurora”B.V. Kozelov, V.E. Ivanov and T.I. Sergienko, Geomagnetism and Aeronomy, Vol. 34,No. 5, (April 1995) (English Translation)“Lyman- Birge- Hopfield bands in proton auroras”Z.V. Dashkevich, B.V. Kozelov and V.Y. Ivanov, Geomagnetism and Aeronomy, vol35, no. 6, (June 1996) (English translation)

“Charge transfer of 0.5, 1.5 and 5keV protons with atomic oxygen: Absolutedifferential and integral cross- sections.” B. G. Lindsay, D. R. Sieglaff, D. A. Schafer, C. L. Hakes, K. A. Smith and R. F.Stebbings, Phys. Rev. A 53, 212 (1996)“Absolute differential cross sections for scattering of keV O- atoms”G.J. Smith, R.S. Gao, B.G. Lindsay, K.A. Smith and R.F. Stebbings, Phys.Rev. A 531581 (1996)“A practical fit formula for ionization rate coefficients of atoms and ions by electronimpact: Z = 1- 28”G. S. Voronov, 1997, Atomic Data and Nuclear Data Tables, 65,1“Absolute differential and integral cross sections for charge transfer of keV O+ withN2”B.G. Lindsay, R.L. Merrill, H.C. Straub, K.A. Smith and R.F. Stebbings, Phys. Rev. A 57,331- 337 (1998)“Absolute partial cross sections for electron- impact ionization of H2, N2 and O2 fromthreshold to 1000 eV”H.C. Straub, B.G. Lindsay, K.A. Smith and R.F. Stebbings, J. Chem. Phys. 108, 109-116 (1998)“Ionization by energetic protons in Thermosphere- Ionopshere ElectrodynamicsGeneral Circulation Model”M. Galand, R.G. Noble, J. Geophys. Res. 104, A12 27,973- 27,989, (December 1, 1999)“Absolute differential and total cross sections for charge transfer of O+ with H2”D. R. Sieglaff, B. G. Lindsay, K. A. Smith and R. F. Stebbings, Phys. Rev. A 59, 3538-3543 (1999)“Absolute differential and integral cross sections for charge transfer of keV O+ ionswith O2”D.R Sieglaff, B.G. Lindsay, R.L. Merrill, K.A. Smith and R.F. Stebbings, Geophys. Res.105, 10,631- 10,635 (2000)“A Self- Consistent Model of the Jovian Auroral Thermal Structure”D. Grodent, J.H. Waite Jr., J- C Gerard, J. Geophys. Res. Vol. 106, A7, 12,933- 12,952July 1 st 2001“Charge transfer of keV O+ ions with atomic oxygen”B.G. Lindsay, D.R. Sieglaff, K.A. Smith and R.F. Stebbings, J. Geophys. Res. 106,8197- 8203 (2001)“Theoretical and experimental studies of the H+- N2 system: Differential cross sectionsfor direct and charge transfer scattering at keV energies”R. Cabrera - Trujillo et al. Phys. Rev. A 66, 042712 (2002)“Electron and Proton Aurora Observed Spectroscopically in the Far Ultraviolet”M. Galand, D. Lummerzheim, A.W. Stephan, B.C. Bush and S. Chakrabarti, J.Geophys. Res. Vol 107, No A7 (2002)“On the dynamics of the Jovian Ionosphere and Thermosphere. III. The Modelling ofAuroral Conductivity”G. Millward, S. Miller, T. Stallard, A.D. Aylward, N. Achilleos, (2002)“Determination of the absolute partial and total cross sections for electron- impactionization of the rare gases”R. Rejoub, B.G. Lindsay and R.F. Stebbings, Phys. Rev. A 65 042713 (2002)“Temperature profiles of Jupiter's Upper Atmosphere”H. Melin, T. Stallard, S. Miller and D. Grodent, Poster, EGS - AGU - EUG JointAssembly, Nice 6- 11 th April 2003“Charge transfer in keV O+(4S,2D,2P)- He collisions”B. G. Lindsay and R.F Stebbings, Phys. Rev. A 67, 022715 (2003)

“Properties of Diatomic Molecules”Hyperphysics - http: / / hyperphysics.phy - astr.gsu.edu /hbase / t ables /dia tomic.html(2004)“Absolute differential cross sections for direct scattering of keV O+ ions by He, N2, H2

and O2”B.G. Lindsay, J. Geophys. Res. 109, A08305,(2004)

“Electron capture and loss by kilo- electron- volt oxygen atoms in collision with He,H2, N2 and O2”B.G. Lindsay, W.S. Yu, K.F. McDonald and R.F. Stebbings, Phys. Rev. A 70, 042701(2004)“On the dynamics of the Jovian Ionopshere and Thermosphere. IV. Ion- NeutralCoupling”George Millward, Steve Miller, Tom Stallard, Nick Achilleos, Alan D Aylward (2004) http: / / r ad med.web.psi.ch /asm /gan try /why_p /n_why_p.htmlTerence Boehringer, Paul Scherrer Institute Proton Therapy information web page,(2005)