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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)  102 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 m3
 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 cm3 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 103 s
~ 104 s
0.6 eV
~1s
~ 0.1s
~ 2 10 3 s
~ 102 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 m3 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,  econd, at T~1 eV
n R2
 econd (T ~ 1 eV) ~
~ (110) 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
 econd (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,  iNcond ,
is comparable to diffusion time (3)
 Therefore, for residual neutral gas density ~ 10 20 m3
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   jin Epot ,
pot
(8)
where Epot ~ 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 Epot  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 fasti ~ 10
16 3
results to the ion beam density n ibeam ~ 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

 ibeam ~  pi n ibeam / n pl

1/ 3
(10)
16 3
 For n ibeam ~ 10 m and n pl ~ 1018 m 3 we find
 ibeam ~ 10 8 s 1
(11)
 Assuming that the frequency of effective collisions of
the beam with residual plasma is of the order of
 ibeam we find a crude estimate of stopping distance
of fast ions caused by collective effects, L ibeam ,
Vibeam
L ibeam ~
~ 10 cm  R
 ibeam
(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 m3 ), 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 ~ (110) 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.
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