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PRMAT

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Electron Collision Processes

Electron atom and electron ion collision cross sections are of crucial importance in the analysis of many laboratory and astrophysical plasmas including those arising in laser-plasma interactions, controlled thermonuclear fusion devices such as tokamaks, planetary atmospheres, stellar atmospheres, gaseous nebulae, active galactic nuclei and supernovae. Over the last twenty-five years a suite of programs based on the R-matrix method have enabled vast amounts of accurate electron collision and opacity data to be calculated by international collaborations, which have had very wide applications. However, in spite of this success, many outstanding problems of importance cannot be treated by these programs which were designed to run on scalar and vector processors. As a result, a completely new parallel program PRMAT has been developed at CCLRC's Daresbury Laboratory [1], which is enabling a new class of electron collision problems, involving many hundreds of coupled target states, to be solved for the first time.

Atomic collisions influence the transport and energy balance in the divertor and edge regions of tokamaks.

Detailed electron-atom collision data is essential for the understanding of the behaviour of plasmas, such as the forbidden lines seen in the Orion nebula.

Electron Collisions

Iron-peak elements

Of particular importance is recent work to obtain accurate collision cross sections for low ionization stages of open d-shell iron peak elements Cr, Mn, Fe, Co and Ni. In the last year a collaboration between CCLRC's Daresbury Laboratory, Queen's University Belfast and the University of Stuttgart has been using PRMAT to study electron collisions with Fe II, Fe III, Fe IV and Fe V [2] (iron has been called the "Rosetta Stone Element" by L.H. Aller because its spectrum offers the wherewithal to interpret the physical conditions in a wide variety of astronomical sources). As part of this work, a detailed convergence study has been carried out for electron Fe II collisions on the Cray T3E at Manchester University. In the figure the collision strength, which is proportional to the cross section, for the transition from the ground state to the first excited state of Fe II is shown in two approximations [3]. The dashed line includes 38 LS coupled target states in the expansion of the total wave function while the full line includes 113 LS coupled target states in this expansion, the latter calculation giving rise to 354 coupled channels (the largest calculation for this target ever carried out). It is clear that the collision strengths in both approximations are dominated by resonances requiring a very fine energy mesh with ~ 20,000 energy values to resolve. Also a very significant difference between the two calculations can be seen below an energy of 0.2 Rydbergs. The resolution of this difference will require the inclusion of further target states in the total wave function. Also, relativistic effects required to resolve transitions between fine-structure levels will give rise to over one thousand coupled target states. It will require the power of the new HPCx machine to provide converged results urgently required by astronomers.

The 5De contribution to the e- - Fe II collision strength for the 3d6 4s a6D - 3d7 a4F transition. Dashed curve , 38-state calculation, full curve 113-state calculation.

References

[1] Sunderland, A.G., Noble, C.J., Burke, V.M. and Burke, P.G., 2002, Comput. Phys. Commun., 145, 311.

[2] Burke, P.G., Noble, C.J., Sunderland, A.G. and Burke, V.M., 2002, Phys. Scripta T100, 55.

[3] Ramsbottom, C. et al, 2002, J Phys B, At.Mol.Opt.Phys, to be published.

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