Some Issues of IFE Chamber Physics Sergei Krasheninnikov University California, San Diego HALP Review Meeting 13-14 November 2001 Introduction After the stage of the fireball expansion, the afterglow phase starts, which is characterized by the cooling of the plasma-gas mixture and the plasma recombinationneutralization processes Usually it is assumed that plasma is almost completely extinguished between the shots (for ~ 0.1 s). However, we show that not the case. Presence of rather high density plasma can significantly alter many processes (e.g. heating of the pellet) In addition, residual plasma can trigger a number of “new” phenomena. For example: heat flux to the pellet caused by the recombination of plasma species can significantly exceed the heat flux of kinetic energy of colliding particles collective interaction of fast ions from the fireball with residual plasma (e. g. beam-plasma instability) which can crucially alter fast ion stopping process Here we just touch some of these very complex issues On the particle density in the chamber Residual particle density, n , (gas and plasma) in the IFE chamber is relatively high: Flux particles into a pump, pump , must equilibrate pellet particle source, pellets , where nVth pump Spump pump pellets f N1 4 (1) 3 where : Vth ~ (1 3) 10 m / s is the thermal speed; Spump ~ 30 100 m2 is the surface of pump duct; pump ~ (1 3) 102 is the pumping efficiency; f ~ 10 Hz is the rep. rate of pellet injection; N1 ~ 10 21 is the number of particles in one pellet From Eq. (1) we find n ~ (1 10) 1019 m3 As a result, the mean free path of neutrals is small N ~ 1 10 cm R chamber ~ 10 m , (2) Notice that the inequality (2) implies: i) short mean free path (fluid) regime of transport and ii) rather weak impact of diffusive effects On residual plasma density Plasma density drop in afterglow phase can be due to: i) volumetric recombination processes (e. g. three body recombination) ii) plasma neutralization at the wall of the chamber However, for the time scale ~ f 1 ~ 0.1s , three body recombination becomes inefficient for the plasma ˜ densities n pl (0.1 1) 1019 cm3 even at a very low temperature ~ 0.1eV : T \ n pl 1018 m 3 1019 m 3 1020 m 3 0.2 eV ~ 0.1s ~ 3 103 s ~ 104 s 0.6 eV ~1s ~ 0.1s ~ 2 10 3 s ~ 102 s Characteristic plasma recombination time, rec 1.2 eV ~ 3s ~ 0.4 s Notice that neutral gas opacity effects, which are not taken into account here, can significantly increase rec The rate of plasma neutralization on the chamber wall is determined by the plasma transport to the wall For the case of diffusive plasma transport to the wall for residual neutral gas density ~ 10 20 m3 we have R2 R2 diff ~ ~3 ~ 0.1s ~ f 1, D plasma iN Vth (3) Thus we see that counting both volumetric plasma recombination and diffusive plasma loss to the wall it is difficult to decrease residual plasma density below n pl ~ 1018 m 3 (or even ~ 1019 m 3 ) (4) It is difficult to estimate the impact of convection effects However, one can expect that that low scale modes of convective motion of gas/plasma mixture are rather quickly dumped by viscosity effects leaving only convective cells with the scale ~ R Then, estimates (3) and (4) can also be applied for the plasma containing within these large convective cells On residual plasma/gas temperature There are three main mechanism of plasma/gas mixture cooling: i) radiation, ii) conduction, and iii) convection Radiation On initial stages of afterglow phase (T > few eV) line radiation is very effective ( L rad (T) ~ 10 25 W cm 3) and plasma cooling is characterized by the time scale ˜ rad (T few eV) ~ T ~ 10 3 s f 1 L(T)n pl However, for the temperatures < 1 eV line radiation loss is negligibly small and rad (T 1 eV) f 1 (5) Be Boron Carbon Neon Argon LZ(Te) (watts cm3) 10-25 10-26 10-27 10-28 1 10 Te (eV) 100 1000 Conduction Electron heat conduction to the walls combined with peripheral electron cooling (e g. electron-neutral elastic collisions) results in the following time scale of the temperature reduction, econd, at T~1 eV n R2 econd (T ~ 1 eV) ~ ~ (110) 10 3 s n pl e Vthe However, due to a strong temperature dependence of electron heat conduction at T ~ 0.1 eV we find econd (T ~ 0.1 eV) ~ 0.3 3 s f 1 (6a) Time scale of the temperature reduction due to heavy particle (ions and neutrals) heat conduction, iNcond , is comparable to diffusion time (3) Therefore, for residual neutral gas density ~ 10 20 m3 we find R2 iN cond ~ 3 ~ 0.1s ~ f 1 i,N Vth (6b) Convection One can expect that that low scale modes of convective motion of gas/plasma mixture are quickly dumped by viscosity effects leaving only convective cells with the scale ~ R Then, estimate (6) can also be applied for the temperature of the plasma/gas mixture containing within these large convective cells Separatrix Convec tive cell Cold Hot Chamber Interesting and important feature of large convective cells is a low temperature of gas/plasma mixture and low plasma density around the separatrix of the flow Large convective cells can be deliberately generated in the chamber and then used to effectively cool the gas and recombine plasma on the pathway of the pellet It easy can be done by shifting the pellet explosion from the center of the chamber, or by a slight asymmetry of the chamber Pellet Exp losion Chamber Center Sepa ratrix Convec tive cell Cha mber Exp losion Asymmetric Chamber Center Pellet Separatrix Asymmetric Cha mber Convec tive cell On heat flux to the pellet Pellet heats up due to radiation flux and collisions with the particles of gas/plasma mixture The heat flux to the pellet associated with kinetic energy of incident particles of gas/plasma mixture is q kin pellet (1 R E ) j in Tg , (7) jin is the flux of incident particles, Tg is the temperature of gas/plasma mixture, is the energy transmission coefficient, and R E is the energy reflection coefficient However, potential energy released at the surface due to surface recombination of atomic particles into the molecules and plasma surface neutralization result in significant addition to the heat flux on the pellet q pellet jin Epot , pot (8) where Epot ~ 4 10 eV is the potential energy associated with the process, is the probability of the process to occur, jin is the flux of corresponding particles Notice that Epot Tg . Therefore, even relatively small content of corresponding atomic particles and plasma in the gas/plasma mixture can significantly alter the heating of the pellet For example, taking into account that the probability of plasma surface neutralization is close to unity and (1 R E ) ~ 1 (for Tg ~ 0.1 eV) we find q neutr pellet pl n pl jin I n pl I kin ~ j T ~ n T n . q pellet in g g (9) where I ~ 10 eV is the ionization potential According to our estimates the residual ionization degree can be ~ 10%. Then from (9) we see that the plasma neutralization can be dominant pellet heating mechanism We notice that for a rather high probability of surface recombination of atoms into the molecules this channel can be even more important since we can anticipate dissociation degree of molecules in gas to be close to 1 On the effect of residual plasma on stopping of energetic ions For all reasonable chamber gas density an impact of binary collisions on stopping of energetic (~ 1 MeV) ions is negligible However, collective effects of the interactions of the beam of energetic ions with residual plasma can significantly alter the population of energetic ions 20 Total number of fast ions per pellet N fasti ~ 10 16 3 results to the ion beam density n ibeam ~ 10 m During pellet explosion the electron temperature of residual plasma can be quickly heated up by electron heat conduction, so that electron temperature of residual plasma exceeds ion one As a result, the ion beam instability can develop, which is characterized by the grows rate ibeam ~ pi n ibeam / n pl 1/ 3 (10) 16 3 For n ibeam ~ 10 m and n pl ~ 1018 m 3 we find ibeam ~ 10 8 s 1 (11) Assuming that the frequency of effective collisions of the beam with residual plasma is of the order of ibeam we find a crude estimate of stopping distance of fast ions caused by collective effects, L ibeam , Vibeam L ibeam ~ ~ 10 cm R ibeam (12) More accurate assessment of the impact of the collective effects on fast ion stopping requires both: i) more accurate description of the evolution of residual plasma parameters as well as ii) more detail evaluation of collective interaction of fast components (both electron and ion) with background one Conclusions Residual density of the gas/plasma mixture is rather high, n ~ (1 10) 1019 m3 ), and results in: i) short mean free path (fluid) regime of transport and ii) weak impact of diffusive effects Analysis of the plasma recombination and diffusion processes shows that it is difficult to reduce residual plasma density below n pl ~ (110) 1018 m 3 While radiation is very effective in gas/plasma energy dissipation for T~ few eV, it does not work for sub eV temperatures. Heat conduction mechanism is not fast enough either. Therefore, it is difficult to expect that averaged temperature of gas/plasma mixture can be reduced to ~ 0.1 eV between the shots. However, the temperature of the gas/plasma mixture near the separatrix of large convective cells can be reduced to ~ 0.1 eV or even below Such cell can be deliberately generated in the chamber. Notice that convective cell can help to track the pellet. Potential energy released on the pellet due to collisions and recombination of atomic and plasma species can significantly exceed the heat flux to the pellet due to just kinetic energy of colliding particles Crude estimate of stopping distance of fast ions caused by collective effects shows that it is feasible to expect that these effects can result in a drastic reduction the population of energetic ions Afterglow plasma physics. After the stage of the fireball expansion, the afterglow phase starts, which is characterized by the cooling of the plasma/gas mixture and the plasma recombination/neutralization processes. Issue: It is assumed that plasma is almost completely extinguished between the shots (for ~ 0.1 s). However, this may be not the case. For the plasma density ~ 1013 cm-3 and gas/plasma temperature range from ~3500 K (~ 0.3 eV) to ~12000 (1 eV) three-body recombination frequency varies from ~ 102 s-1 to 10 s-1 (recombination rate constant varies from ~ 10-11 cm3-s-1 to ~ 10-12 cm3-s-1). Plasma diffusion time to the wall of a chamber with radius ~10 m and gas density ~ 1014-15 cm-3 is > 0.1-1 s. As a result one can expect that residual plasma density can be about 1012-13 cm-3. Presence of rather high density plasma can significantly alter many processes such as metal condensation and heating of the target while it moves through the gas/plasma mixture. In addition, residual plasma can trigger a number of a new phenomena. For example, thermal instability of the gas/plasma mixture which causing strong striation of the mixture which may affect laser beam propagation. Another example is the collective interaction of fast ions from the fireball with residual background gas discussed below. Expansion of the fireball into background gas/residual plasma and slowing of fast ions. Issue: For the background gas/residual plasma density ~ 1014-15 cm-3 the slowing distance of energetic (~ MeV) ions due to binary collisions with background gas/residual plasma particles exceeds chamber radius (~ 10 m). However, collective effects associated with fireballbackground plasma instabilities (e.g. two stream instability) can be much more important mechanism for the reduction of the population of energetic ions. Background plasma can be either residual or due to gas ionization by fireball particles and radiation. External magnetic field or remains of magnetic field wish can be self-generated on the stages of pellet compression/burn can significantly alter and, probably, enhance, collective effects of fireball-background plasma interactions.