Outline. 1. Introduction (FI3, previous works). 2. Fast Electron Generation ⦠PIC a. Effect of Density gap at rear surface of cone tip b. Density profile steepening at ...
S8-6
Holistic Simulation for FIREX Project with FI3
T. Johzaki1, H. Sakagami2, H. Nagatomo1, K. Mima1 1
Institute of Laser Engineering, Osaka Univ., Japan 2 Theory and Computer Simulation Center, National Institute for Fusion Science, Japan
Outline 1. Introduction (FI3, previous works) 2. Fast Electron Generation … PIC a. Effect of Density gap at rear surface of cone tip b. Density profile steepening at LPI region c. Pre-plasma scale length dependence 3. Core Heating ………………….RFP-Hydro 4. Fast Ion Contribution ……… PIC -> RFP 5. Summary
3rd 3rd Int. Int. Conf. Conf. on on the the Frontiers Frontiers of of Plasma Plasma Physics Physics and and Technology Technology March 5 9. 2007, Amari Atrium Hotel, Bangkok, Thailand March 5-9. 2007, Amari Atrium Hotel, Bangkok, Thailand
1/21
Background : Necessity of Integrated Simulation
Fast Heating Experiments at ILE Fast Heating of Cone-Guided CD Targets with GEKKO PW Laser at ILE R. Kodama, et al., Nature 418, 933 (2002)
Neutron yield was enhanced by 3 orders of magnitude.
Heated core up to ~ 0.8keV.
1-D FP*
*) 1-D Fokker-Planck simulations results
As the next step, FIREX project has been started. However, efficient heating mechanism is not clarified yet!! 2/21
FI FI33 Project Project Fast Ignition Integrated Interconnecting code Project H. Sakagami and K. Mima, Laser Part. Beams, 22 (2004) 41.
Radiation-Hydro code “PINOCO” Collective PIC code “FISCOF”
Implosion Dynamics
Relativistic LPI cone – core profiles
t en r ur es k c Pl rn rofil as u t Fokker-Planck – Hydro code “FIBMET” es e dp m En f il R o a l Core heating er pr pr Fie gy n of ile t ro es de c 10nc e s l po il t e prof sit s io n Fa eld Fi
Bu l
Osaka Univ., NIFS, Kyushu Univ. Setsunan Univ.
T. Yokota, WO15.2
100nc
Data flow considered planed
3/21
Previous work Density gap effect at rear surface of cone tip ~ 2000n cr ignitio n las e r ~
Fast electron current generates the strong static field, which traps relatively low energy fast electrons inside the cone tip and accelerates the bulk electrons into the cone tip. => Fast electron energy is moderated and the beam duration becomes long. Due to the density gap effects, the dense core is heated more efficiently. But, the heated core temperature is ~ 0.5keV, which is still lower than the experimentally measured value, 0.8keV. 4/21
Density gap + Pre-plasma scale length • The pre-plasma scale length, which is determined by the pre-pulse of heating laser, may strongly affects the laser-plasma interactions. (previously fixed as 5µm) • The effects of density gap + pre-plasma scale length are evaluated by 1D simulations (PIC + RFP-Hydro).
1D FP-Hydro simulations “FIBMET” Evaluation of core heating using fast electron profiles obtained by 1D-PIC and bulk plasma profiles obtained by 2-D implosion simulations “PINOCO”
1000
Observation Point (1) (2)
100 Density [n/nc]
1D PIC simulations “FISCOF1” evaluation of effects of density gap and pre-plasma scale length on the fast electron profiles
20
10 1 0.1 0.01 -40
ex/Lf (Lf:0~ 5) -20
ex/10
10nc
0 20 Distance [µm]
40
60 5/21
Simulation Condition for 1D “PIC FISCOF1” Laser-Plasma Interactions at the Cone Inner surface Electrons and ions are mobile. All the ion are Au with real mass and Z=50 Collision is not included. Cone tip is modeled by 100nc plasma Heating laser parameters: 1000 Observation Point (1) – λL = 1.06 [µm] (2) 100 – Gaussian profile ex/10 10 20nc – τFWHM= 750 [fs] 1 10nc 20 2 – IL = 10 [W/cm ] ex/L Density [n/nc]
• • • • •
0.1
0.01 -40
f
(Lf:0~ 5) -20
0 20 Distance [µm]
40
60 6/21
Density Steepening at LPI region
80
At the front surface (LPI region)
10µm
1000 100
px/mec
• The pre-plasma is pushed by the strong Ponderomotive force and then the density profile steepening occurs. • Periodically lunched electron bunches are observed, and returned electrons are completely kicked back.
Lf = 1µm
10 1
0
Electron density ne/nc
Strong Ponderomotive force steepens the density profile.
0.1
At the rear surface (density gap) • The static field built up due to fast electron current, which reflects the relatively lowenergy fast electrons and accelerates the bulk electrons into the cone tip.
at t = 1ps 7/21
Effects of density gap & profile steepening (Lf = 1µm) Energy Spectra
f(E ) [a.u.]
Forward-directed fast electron beam intensity 20
fe
inside cone 20nc point
2
Intensity [W/cm ]
10
10
51
10
50
10
49
10
48
1~1.5ps in s id e c o n e 2 0 n c p o in t
19
10
47
51 1100
f(E ) [a.u.]
18
fe
10
17
10
0
1
2
3
Time [ps]
4
5
10
50
10
49
10
48
10
47
2.5~3ps in s id e c o n e 2 0 n c p o in t
6 0
1
2
3
4
E n e r g y , E f e [M e V ]
• The relatively low energy fast electrons are trapped inside the cone tip due to the static fields generated at the front and rear surfaces of cone tip. • These trapped electrons are released from the tip even after finishing laser irradiation. 8/21
Scale length dependence 1 Strong Ponderomotive force steepens the density profile. Short scale length case • The pre-plasma is swapped away. • Periodically lunched electron bunches are observed, and returned electrons are completely kicked back.
Long scale length case
Electron momentum px/mec
80
10µm
10µm
10µm
1000 100 10 1
0
0.1 Lf = 0.25µm
Lf = 1µm
Electron density ne/nc
• The pre-plasma still remains at LPI region. • Very high energy fast electrons are generated and part of the returned electrons are pulled into the vacuum region.
Lf = 5µm
at t = 1ps
9/21
Scale length dependence 2 With increasing the scale length, higher energy electrons generated.
• Lf = 1µm; the relatively low energy electrons, which are favorable to core heating, are increased due to the gap and steepening effects.
1E54 observed at 20nc
1E53 f(E) [a.u.]
• Lf = 5µm; very high energy electrons are not trapped and trapped effect due to density gap and profile steepening is weaker. So the fraction of high energy electrons is large. They can not heat the core efficiently due to long range.
Time-integrated Fast electron spectrum
Lf=0µm
1E52
Lf=1/4µm
1E51
Lf=5µm
Lf=1µm
1E50 1E49
0
2
4 E [MeV]
6
Optimum scale length for core heating will exist!!
8
10/21
1D Fokker-Planck Simulation Model Fast Electron & Ion Transport
Fast Electron & Ion Profiles （PIC Code）
Relativistic Fokker-Planck transport Electric Fields (x) – CIP (85x161 mesh) (p) – Discontinuous Linear FEM (25 groups) (µ) – Discrete Ordinate Sn method (36 directions)
3.0
10 100
2.5
80 8
2.0
60 6
1.5 1.0
40 4
Te Ti
0
20
40
Energy(fast electron, ion ) & Momentum(fast ion) deposition rates
Radiation-Hydrodynamics
20 2
0.5 0.0
ni , Ti , Te ,Z ρ [g/cc]
T [keV]
Fast electrons were injected at outer surface of a gold cone.
60
80
X
Imploded Core Profiles （ALE Rad-Hydro Code）
0 100
Bulk Plasma ・1-fluid 2-temp. CIP code Radiation ・ Flux-limited diffusion 11/21
Core Heating Properties (1D RFP) Core Heating Properties…1D FP
source: Lf = 1µm, nerear = 10nc
Heating rate (at t = 2.5ps)
• The Coulomb interaction with bulk electron is dominant energy deposition mechanism of fast electron in dense core. • The bulk ion is heated through the temperature relaxation with bulk electron, so Ti reaches maximum by 3ps delay from Te,max time.
100
Total Coulomb(short) Coulomb(long) Joule
80 60
1E26 40
ρ [g/cc]
Pdep [W/m3]
1E27
20 1E25
0
20
40 60 X [µm]
80
0 100
Temporal evolution of spatially-averaged Temp (t), (t) [keV]
1.4 1.2 1.0
Whole region
0.8 0.6
Core(ρ0>10g/cc)
0.4
0.2
0 1 2 3 4 5 6 7 8 9 10 Time [ps]
Averaged ion temperature reaches ・ 0.87keV at 9,0ps in the whole fuel region, ・ 0.72keV at 6.5ps in dense core （ρ>10g/cc) . → ∆Ti ∼0.35keV 12/21
Pre-plasma scale length dependence : Lf=0 ∼ 5 µm Core Heating Properties…1D FP Irradiated Laser Energy = 79.8 MJ/cm2
2
30
20 20
15 10
10 5
max [keV]
25
1.2
Coupling Efficiency [%]
30
Energy [MJ/cm ]
Maximum values of Spatially averaged ion temperature
Injected Fast Electron Total E < 2MeV
whole core
1.0 0.8 0.6 t=o, whole
0.4
t=0, core
Deposited in Fuel
0
0
1
2
3
Lf [µm]
4
5
0
0.2
0
1
2
3
4
5
Lf [µm]
• Lf < 1µm; ηL→e is small, so that the core heating efficiency is low. • Lf > 2µm; with increasing Lf, ηL→e gradually decreases, but the low energy component (E < 2MeV) decreases faster, which lowers the core heating efficiency.
In the present simulations, the optimum Lf for core heating is 1.5µm. The energy coupling from laser to core is 14.9%, and the core temperature reaches 0.86keV (∆Ti = 0.48keV).
13/21
Pre-plasma estimation by PINIOCO An Example of PINOCO Simulation for pre-plasma formation due to pre-pulse irradiation (~1011W/cm2)
ne / nc
1000
L = 0.65µm L = 0.45µm
Te [eV]
ne / nc
Pre-pulse
10 1
initial solid surface
y [µm]
100
y=20µm y=15µm y=10µm y= 5µm y= 0µm
L > 10µm
0.1 40
45
50
55
60
65
70
X [µm]
x [µm]
Pre-plasma has double scale length, i.e. Lf1 ≤ 1µm at ne > nc and Lf2 >> 1µm at ne < nc. 14/21
Double Scale a Length;
(Lf1=1µm (ne>nc)+ Lf2=5µm(nenc)+ Lf2=5µm(ne＜nc)) Core Heating Properties…1D FP
Temperature [keV]
1.1
1.0 0.9
Double scale
0.8
Single 1µm
0.7 0.6
Single 5µm
0.5
Irradiated Laser Energy = 79.8 MJ/cm2 Lf[µm]
Single scale 1.0 5.0
Double scale 1.0+5.0
Ebeam[MJ/m2] ηL→e [%]
21.0 26.3
21.2 26.6
24.6 30.8
Edep [MJ/m2] ηe→fuel [%]
8.68 41.3
4.42 20.8
10.94 44.5
ηL→fuel [%]
10.9
5.5
13.7
0.17
0.46
0.4 0.3
0
2
4
6
8
10
∆max[keV] 0.34
Time [ps]
In the double scale case, the number of relatively low energy electrons (Enc)+ Lf2=5µm(ne＜nc)
double scale
n r = 10n c
35
Total E < 2MeV
30
25 20
20
15 10
10
1.0
max [keV]
30
ηL→fuel , ηL→e [%]
2
Fast electron energy [MJ/cm ]
○○△
double scale single scale
0.8 0.6 t=0
0.4
5 0
0
1
2
3
L f [mm]
4
5
0
0.2
0
1
2
3
4
5
Lf [µm ]
In the double scale case, low energy component (E>1µm), with increasing Lf, the low energy component of fast electron, that mainly contributes to the core heating, becomes small, so that the heating efficiency also becomes low. • Optimum scale length is 1.5µm
1.0
max [keV]
• When scale length is too short (Lf nc) + Lf2 = 5µm (ne < nc); ηL→fuel ~17%, max = 0.95keV 18/21
Others Longer & Higher energy Laser Case (>10ps, >1020W/cm2) • In FIREX-I, heating laser is 10kJ/10ps. For ignition, 100kJ (or more?) heating laser is required. What’s happen? Can we Extrapolate the short & relatively low energy shot results? Additional Heating due to Fast Ion ? • Accelerated ions (Au, Z=50) does not contribute to the core heating because of their short range. • But, how about the different ion species (C, P, D, T)? Geometrical effects in laser-cone interactions (e.g. laser-cone wall interaction, laser focusing, fast electron accumulation) ・・・・ On going by T. Nakamura Collision processes in the cone ・・・・ reduced model is under construction. Effects of Microscopic instabilities on fast particle transport • In ps-order 1D PIC simulations, we observed ion heating (or acceleration) in the medium-density propagation region (between cone tip and core, n ~ a few 10nc region) due to the instability. 19/21
