The Particle-in-Cell (PIC) method was used to study heat flux mitigation experiments with argon. In the experiment it was shown that a magnetic field allows to reduce the heat flux towards a target. PIC is well-suited for plasma simulation, giving the chance to get a better basic understanding of the underlying physics. The simulation demonstrates the importance of a self-consistent neutral-plasma description to understand the effect of heat flux reduction

Bandelow, G.

Duras, J.

Kahnfeld, D.

Kemnitz, S.

Konigorski, D.

Lüskow, K. F.

Schneider, R.

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

Plasma Physics and Technology 3(3):110–115, 2016 © Department of Physics, FEE CTU in Prague, 2016PARTICLE-IN-CELL SIMULATION CONCERNING HEAT-FLUXMITIGATION USING ELECTROMAGNETIC FIELDSLüskow K. F. a,∗, Kemnitz S.a,c, Bandelow G.a, Duras J.a,Kahnfeld D.a, Schneider R.a, Konigorski D.ba Ernst-Moritz-Arndt University Greifswald, Institute of Physics, Felix-Hausdorff-Str. 6, 17487 Greifswald,Germanyb Airbus Operations GmbH, Emerging Technologies & Concepts, Kreetslag 10, 21129 Hamburg, Germanyc University Rostock, Institute of Informatics, Albert-Einstein-Str. 22, 18059 Rostock, Germany∗ lueskow@physik.uni-greifswald.deAbstract. The Particle-in-Cell (PIC) method was used to study heat flux mitigation experimentswith argon. In the experiment it was shown that a magnetic field allows to reduce the heat fluxtowards a target. PIC is well-suited for plasma simulation, giving the chance to get a better basicunderstanding of the underlying physics. The simulation demonstrates the importance of a self-consistentneutral-plasma description to understand the effect of heat flux reduction.Keywords: Particle-in-Cell, argon, heat-flux mitigation, electromagnetic fields.1. MotivationIn space missions an enormous amount of money isspent for the thermal protection systems for re-entry.To minimize these costs one is interested in findingnew ways of reducing the heat flux. The idea is touse magnetic fields to guide the flux away from there-entry vehicle. In 2002 the European Space Agency(ESA) started an investigation on heat flux mitigationby means of MHD in partially-ionized argon-flows.Argon was chosen for first-principle tests, becauseit is a noble gas and inert. Therefore, additionalcomplications from complex chemistry — like in air —do not appear, simplifying the analysis of such tests.A strong heat flux reduction was measured, createdby an externally applied magnetic field [1]. In thepast Navier-Stokes fluid codes for the neutrals wereapplied combined with rather crude models for theplasma components. Such models were not able toreproduce the experimental observations. With thehelp of a kinetic particle method one expects to geta more realistic description of the system, includingneutrals and plasma. Therefore, a Particle-in-Cellcode with Monte-Carlo Collisions (PIC-MCC) wasdeveloped.2. Code description and simulationset-upThe code uses the well-established Particle-in-Cellmethod combined with Monte-Carlo collisions (PIC-MCC). PIC was successfully applied in various fieldsof plasma physics to obtain a better physical un-derstanding. PIC-MCC simulation delivers a fullyself-consistent microscopic description of a plasma.Therefore, all plasma-parameters (macroscopic andmicroscopic) can be diagnosed. In particular, entitieslike potential, densities, temperatures, velocity distri-bution functions and power fluxes can be calculated.A more detailed description of the method itself canbe found in different reviews [2, 3].So-called “super-particles” are used, each of themrepresenting a number of real physical particles. All ofthem follow the same trajectory due to the fact thatthey have the same mass-to-charge ratio and thereforethe same acceleration by the Lorentz force. The par-ticles move in the self-consistent electric field whichis calculated on a spatially equidistant grid from thePoisson equation, which itself is determined by thespace charge deposited by the pseudo-particles andthe applied boundary conditions. The real mass ratiobetween electrons and ions is used. Particle collisionsare handled by Monte-Carlo collisions (MCC) routines,that change particle-velocities according to the under-lying collision dynamics. All relevant collision typesare implemented in the code: electron-neutral elastic,ionization, excitation, coulomb collisions, ion-neutralmomentum transfer and charge exchange. Neutralsare treated as plasma particles with zero charge. This,in fact, means that the neutral model is a DirectSimulation Monte-Carlo (DSMC) description.In the model two spatial (axial and radial) andthree velocity components (2d3v) are resolved. Thecomputational domain is a region of 42 cm in axialand 14 cm in radial direction. It consists of a particlesource on the left boundary and a target on the right,both lying directly at the symmetry axis. All particlescrossing the symmetry axis get reflected. The faceof the blunt body target is placed at 26 cm, it has aradius of 3.6 cm. The blunt body is implemented asmetallic, but is covered by a dielectric surface madeof quartz ( = 4.27). The left domain boundary has afixed potential of 0.5V to represent the exit of the arc-110vol. 3 no. 3/2016 PIC Simulation of heat-flux mitigationFigure 1. Magnetic field used for the current simula-tion domain.jet used for the experiment and ensures that particlesinjected here move towards the target. The upper andthe right domain boundaries are set to zero potential.The magnetic field was calculated using the Finite-Element Magnetic Method solver (FEMM) [4]. Thetopology of the dipole-like magnetic field is shown infigure 1.At outer domain boundaries all particles get ab-sorbed. The same procedure is done for plasma par-ticles at the target. Secondary electron emission canbe neglected due to the small emission coefficient ofquartz (< 0.5) at low energies [5]. Neutrals are re-flected at the target surface, because it is assumedthat noble gases are inert to chemical reactions.A uniform background density is combined witha local particle source at the left side of the domain.The neutral gas density reproduces the backgroundpressure from the experiment that is not created bythe source but is an artifact of the non-perfect vacuumcreation in the test-chamber.The number of particles injected in each timestepwere adjusted in order to reach the measured den-sity from the experiment (ne = ni ≈ 2.8 · 1011 cm−3,nn ≈ 1.6 · 1015 cm−3). Neutrals are injected witha maxwellian-distributed velocity with a drift of2070 m/s to represent the free stream velocity mea-sured by microwave interferometry. Ions have similarsource velocities as neutrals. Electrons are injectedwith a two temperature energy distribution. The mainpeak of the distribution function is at 0.7V which isthe measured averaged electron temperature from ex-periment. Due to the strong emission of light duringexperiment one also needs hot tail electrons that arerepresented in the simulation by a second distributionat higher energies but with lower particles numbers.This is a typical feature of plasma sources, for examplein RF plasmas [6]. The high energy tails exist becausethe mean free path of such electrons are longer thanthe source dimension and non-Maxwellian distributionfunctions can sustain. A plot of the energy distribu-tion functions that is injected in the simulation canbe seen in figure 2.To optimize numerical performance the size of thedomain is scaled down by a factor of 100 preservingthe ratios of system lengths to gyroradii and mean freepath. As a consequence of similarity scaling densitiesand the magnetic field are increased by the sameFigure 2. Electron energy distribution injected by theparticle source.factor. This ensures the correct physical behavior ofall particles.The large difference between neutral and plasmadensity leads to a problem in computational resourcesdue to the large number of neutral particles if thesame pseudo-particle factor is applied to neutrals andplasma. Fortunately, the ionization threshold energy isbeyond the measured electron temperature, so one canconsider the ionization as negligible. Therefore, oneis allowed to implement an additional scaling factorfor neutral super-particles. For the current simulationan additional weighting factor of 103 is applied. Theweighting factor linearly increases the cross-section forevery collision in which one neutral is involved. Thecross section for neutral-neutral collisions is multipliedby the square of the weighting factor.According to experimental observations there arestronger fluctuations setting in by applying the mag-netic field than in the unmagnetized case. To take thisinto account in the simulation a radial diffusion modelwas implemented for the magnetized case. A diffusioncoefficient of 10m2 s−1 is used for plasma particles.For neutral particles a coefficient of 0.1m2 s−1 is set.This estimate is based on diffusion coefficients frommagnetic fusion [7]. It is well-known that turbulence ina plasma can be created or at least can be enhanced bymagnetic fields [8]. Without activating the turbulenceall particles move towards the center of the target andthe flux will be strongly increased in contrast to theexperiment.3. Results3.1. Comparison of the simulation withexperimentTo ensure that the simulation represents the correctphysics as observed in the experiment, one has to com-pare the results from the simulation with the measure-ments from the experiment. Unfortunately, plasmaparameters are not well diagnosed in the experimen-tal campaign. One has only line-averaged values forelectron temperature and density. The electron den-111Lüskow K. F. , Kemnitz S., Bandelow G. et al. Plasma Physics and TechnologyFigure 3. Electron density without (top) and with (bottom) magnetic field.Figure 4. Neutral density without (top) and with (bottom) magnetic field.112vol. 3 no. 3/2016 PIC Simulation of heat-flux mitigationFigure 5. Distribution function of the axial velocity component for neutral particles without (top) and with (bottom)magnetic field.Figure 6. Number of charge exchange collisions per second without (top) and with (bottom) magnetic field.113Lüskow K. F. , Kemnitz S., Bandelow G. et al. Plasma Physics and Technologysity ne in the experiment was measured by microwaveinterferometry with the result of 2.8 · 1011 cm−3 [1].The simulated density averaged over the region wherethe measurement takes place is 1.8 · 1011 cm−3 for thecase without magnetic field. In figure 3 the electrondensity is shown with and without magnetic field.In accordance with the experiment one can see apush-back of the region of high electron density fromthe target. This is in good agreement with the shrink-ing of the bright emission region from experiment [1].In addition, the density distribution is changed signif-icantly and in front of the target a region of higherdensity occurs. Experimentally, an additional brightemission region near the target appears when a mag-netic field is applied.In contrast to plasma parameters the neutral gasdynamics is very well characterized. The averagedneutral density in experiment was 1.6·1015 cm−3. So itis about 4 orders of magnitude larger than the electrondensity. The simulated neutral density distributioncan be seen in figure 4. In good agreement with theexperiment without magnetic field a clear shock frontat the target is obtained. The average velocity ofneutrals in this region is decreasing from supersonic(about 2 500 m/s) to less than 1 000 m/s. The originalsharp shock front in the case without magnetic fieldgets broadened in the case with magnetic field. Thisbroadening is a combination of very strong chargeexchange collisions and radial anomalous turbulenttransport introduced as described before. The trian-gular shape of the neutral density in the case withmagnetic field is a consequence of the plasma speciesreacting to the magnetic field. Electrons are magne-tized and follow the magnetic field. They get pushedtowards the front side of the target, where they accu-mulate. The increased turbulent transport leads toa radial triangular structure of this increased densityregion reflecting also the structure of the magneticfieldlines. Ions follow electrons due to quasi-neutralityand pile up there as well. Charge exchange collisionscouple this density increase in the plasma speciesto the neutrals. Therefore, this triangular structurebuilds up for neutrals as well. It would be interestingto check, whether this triangular shape in density andthe broadening of the shock front is also detectablein experiment. Indications are existing in the exper-iment, because the shock front practically vanishedin the case with magnetic field in the photos (seeFigure 6 of [1]).The simulated axial velocity distribution fromDSMC is shown in figure 5 summed over all neu-trals with the same axial position independent of theirradial position. One can see that the main peak isat about 2 000m s−1 similar to the experimentally ob-served velocity of 2 350m s−1. In front of the targetthere are neutrals with negative axial velocities. Theseneutrals originate from reflection at the target as de-termined by collisional effects in the solid (collisionalcascades).The velocity distribution function for ions in Fig-ure 7 looks very similar to the one for neutrals. Thisresembles the strong coupling by charge exchangecollisions.3.2. Heat Flux ReductionThe most important finding from experiment was thestrong heat flux mitigation by activating the mag-netic field. Due to the relative small electron andion densities compared to the neutral density one canestimate that most of the heat flux towards the targetis carried by the neutrals. Up to now the reason forthe strong heat flux reduction by an magnetic fieldwas not understood, because there exists no obviousdirect coupling between B-field and neutral particledynamics.In the simulation results a significant change in theneutral velocity distribution function appears whenthe magnetic field is activated. In front of the targetthere are more particles with negative axial velocitiesthan in the case without magnetic field. An expla-nation for this can be found in the coupling to themovement of plasma particles.Electrons moving towards the target experiencemagnetic field gradients redirecting them towards theaxis. As a consequence a redistribution of electrondensity with an increased density near the axis evenin front of the mach cone is appearing. Due to quasi-neutrality the ion density needs to be similar to theelectron density. Argon has the characteristics of veryhigh charge exchange cross-sections. Therefore, theincreased ion density in front of the mach cone leadsto more charge-exchange collisions that modify thevelocity of the neutrals, see figure 6.This shows up as an increased region of negative ve-locities in the axial velocity distributions (see figure 5).As a consequence, the averaged neutral velocity getsreduced compared to the case without magnetic field.The total heat flux profile is summed up over allspecies contributions (electrons, ions, neutrals). Itis dominated in this case by the neutral component.Therefore, less neutral flux reach the target and thetotal heat flux is reduced, see figure 8. The charge-exchange collisions act as a parallel momentum sinkfor the neutral flow slowing it down. The integralreduction of the total heat flux can be calculated byintegrating the flux over the target in radial direction.The result is a mitigation to 57% of the original heatflux without magnetic field. The measured heat fluxreduction was 85% with rather large experimentaluncertainties.4. ConclusionsIn the frame of this study a PIC-MCC code was devel-oped to simulate a heat flux mitigation experimentalcampaign performed by DLR 2007. The main resultof the experimental campaign was the demonstrationto reduce the total heat flux by externally applied114vol. 3 no. 3/2016 PIC Simulation of heat-flux mitigationFigure 7. Distribution function of the axial velocity component for ions without (top) and with (bottom) magnetic field.Figure 8. Simulated radial profile of the total heat fluxon the target.magnetic fields. This effect was qualitatively repro-duced by PIC-DSMC simulations for the first time.A possible explanation for the effect was found by anincrease of charge exchange collisions between plasmaions and neutrals. This shields the target from the im-pinging neutral particles acting as a momentum sinkfor the neutral gas flow. The increased ion densitydriving this effect is also affected by increased radialturbulent transport observed experimentally in themagnetized plasma and taken into account also in themodel.AcknowledgementsThis work was supported by the German Space AgencyDLR through Project 50RS1508.References[1] Ali Gülhan, Burkard Esser, Uwe Koch, Frank Siebe,Johannes Riehmer, Domenico Giordano, and DetlevKonigorski. Experimental verification of heat-fluxmitigation by electromagnetic fields inpartially-ionized-argon flows. Journal of Spacecraft andRockets, 46(2):274–283, 2009.[2] Charles K. Birdsall and A. Bruce Langdon. Plasmaphysics via computer simulation. CRC Press, 2004.[3] D. Tskhakaya, K. Matyash, R. Schneider, andF. Taccogna. The particle-in-cell method. Contributionsto Plasma Physics, 47(8-9):563–594, 2007.[4] David Meeker. Finite element method magnetics.FEMM, 4:32, 2010.[5] A Dunaevsky, Y Raitses, and NJ Fisch. Secondaryelectron emission from dielectric materials of a hallthruster with segmented electrodes. Physics of Plasmas(1994-present), 10(6):2574–2577, 2003.[6] VA Godyak and RB Piejak. Abnormally low electronenergy and heating-mode transition in a low-pressureargon rf discharge at 13.56 mhz. Physical review letters,65(8):996, 1990.[7] F Perkins, P Barabaschi, D Boucher, JG Cordey,A Costley, J Deboo, PH Diamond, N Fujisawa,CM Greenfield, J Hogan, et al. Iter physics basis. InPlasma Physics and Controlled Nuclear FusionResearch: Proceedings of the... International Conferenceon Plasma Physics and Controlled Nuclear FusionResearch, volume 15, page 477. International AtomicEnergy Agency, 1994.[8] D. Bohm, E. Burhop, H. S. W. Massey, andR. Williams. The characteristics of electrical dischargesin magnetic fields. National nuclear energy series:Electromagnetic Separation Project. McGraw-Hill, 1949.115

Particle-in-cell Simulation Concerning Heat-flux Mitigation Using Electromagnetic Fields

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Particle-in-cell Simulation Concerning Heat-flux Mitigation Using Electromagnetic Fields

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