Transcript 5th International Conference on the Frontiers of Plasma Physics and Technology 18-22 April 2011, Singapore MULTI-RADIATION MODELLING OF THE PLASMA FOCUS Sing Lee 1,2,3 and.

5th International Conference on the Frontiers
of Plasma Physics and Technology
18-22 April 2011, Singapore
MULTI-RADIATION MODELLING OF
THE PLASMA FOCUS
Sing Lee 1,2,3 and Sor Heoh Saw 1,2
1INTI
International University, 71800 Nilai, Malaysia
2Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia
3Nanyang Technological University, National Institute of Education, Singapore 637616
e-mails: ; [email protected]; [email protected]
Outline of Talk-Applications of Plasma
Focus Radiation
• The Plasma Focus: wide-ranging application
potential due to intense radiation
• Modelling using Lee Model code for
operation in various gases: D, D-T, He, Ne, N,
O, Ar, Kr and Xe.
Outline of Talk: Role of Radiation Cooling for
Neutron Yield Enhancement
• Various gases used for fusion neutron yield enhancement e.g.
Kr-doped Deuterium
• Suggested mechanism: thermodynamically enhanced pinch
compressions- generally found insufficient
• This paper considers effect of radiation cooling and radiation
collapse in the heavier noble gases.
• In gases undergoing strong line radiation the “equivalent
Pease-Braginskii” radiation-cooled threshold current is
lowered from the Hydrogen IP-B of 1.6 MA..
• The Lee Model code is used to demonstrate this lowering.
• It is suggested that the neutron enhancement effect of Krdoped Deuterium could at least in part be due to the enhanced
compression caused by radiation cooling induced by the
dopant.
The Plasma Focus
1/2
 Plasma focus: small fusion device, complements international
efforts to build fusion reactor
 Multi-radiation device - x-rays, particle beams and fusion
neutrons
 Neutrons for fusion studies
 Soft XR applications include microelectronics lithography and
micro-machining
 Large range of device-from J to thousands of kJ
 Experiments-dynamics, radiation, instabilities and non-linear
phenomena
Applications
SXR Lithography
• As linewidths in microelectronics reduces
towards 0.1 microns, SXR Lithography is one
possibility to replace optical lithography.
• Baseline requirements, point SXR source
– less than 1 mm source diameter
– wavelength range of 0.8-1.4 nm
– from industrial throughput considerations,
output powers in excess of 1 kW (into 4p)
15
SXR lithography using
NX2 (Singapore) in Neon
1.0
1
intensity (a.u.)
0.8
0.6
2
a
b
0.4
3
0.2
7
98
0.0
8
9
10
65
4
11
12
13
14
wavelength (Å)
16
Radial Compression (Pinch)
Phase of the Plasma Focus
Lines transferred using NX2 SXR
X-ray masks in Ni & Au
SEM Pictures of transfers in AZPN114 using NX2 SXR
18
1. Complementary modelling of NX2 SXR
production mechanism and optimum regime
Modelled Mechanisms
Optimum Regime
Computed vs Measured
The Plasma Focus –Lee Model code
Axial Phase
Radial Phases
The 5-phases of Lee Model code
Includes electrodynamical- and radiation- coupled
equations to portray the REGULAR mechanisms of
the:
• axial (phase 1)
• radial inward shock (phase 2)
• radial RS (phase 3)
• slow compression radiation phase (phase 4)
including plasma self-absorption
• the expanded axial post-pinch phase (phase 5)
Crucial technique of the code: Current Fitting
2. Modelling Xenon PF for EUV
• Change pressures, to go from regular
high speed mode to very slow highly
radiative mode
• Pressure range: 0.1 to 5 torr
• An aim could be to determine the
conditions for good EUV yield (standard
NGL wavelength set at 13.5nm-Xe IX Xe
X
Xe XI suitable for yielding EUV)
• XePFNumerical Expts.xls
Calculate Zeff for Temperature T, first calculate
the ionization fractions, an (n=0 to 54) using
Ionization Potential data from NIST
Xenon ionization Fractions Corona Model
Ionization Fractions
1
0.8
0.6
0.4
0.2
0
-1.00
0.00
1.00
2.00
3.00
4.00
Log(10) of T in eV
5.00
6.00
7.00
From the an, calculate Zeff
Zeff of Xenon Corona Model
50
Zeff
40
30
20
10
0
0.00
1.00
2.00
3.00
4.00
Log(10) of T in eV
5.00
6.00
7.00
Sp Ht Ratio g =(f+2)/f
• Computation of f and g
2
 a r U r   a r U er 
f = 3+ m
( R o /M)TD
1

  a r U er 
g
5 m a rU r
= +
g -1 2
( R o /M)TD
Compute Specific Heat Ratio g needed for
calculating the radial dynamics
To show the relative effects of PBrems, PRec, PLine
& opposing PJoule for Xenon
Power factors-Pink :Lines Radiation; Blue:Recombination;
Oange:BremsStrahlung;
Red: Total Radiation; Black: Joule Heating (1 torr anode radius, a=1 cm)
Radiation Rate Factors
1.00E+09
Typical PF Operation left of arrow
1.00E+07
1.00E+05
1.00E+03
1.00E+01
1.00E-010.00
-1.00
1.00E-03
1.00
2.00
3.00
1.00E-05
1.00E-07
Log10 T in eV
4.00
5.00
6.00
Conclusion for that work
• Radiative Plasma Focus Model & Code extended
to include:
Xenon with Radiative Collapse Phase
• Computes condition for good EUV yield- very
slow dynamics required in Xenon PF;
• Thus PF may not be advantageous for such
Xenon EUV production
3. Kr-doped Deuterium
Order of magnitude enhancement in neutron emission with
deuterium-krypton admixture in miniature plasma focus device
Rishi Verma1, P Lee1, S Lee1, S V Springham1, T L Tan1, R S Rawat1, M. Krishnan2
1National Institute of Education, Nanyang Technological University, Singapore
2Alameda Applied Sciences Corporation, San Leandro, California 94577, USA
Appl. Phys. Lett. 93, 101501 (2008); doi:10.1063/1.2979683 (3 pages)
The effect of varied concentrations of deuterium-krypton (D2–Kr)
admixture on the neutron emission of a fast miniature plasma focus
device was investigated. It was found that a judicious concentration
of Kr in D2 can significantly enhance the neutron yield. The
maximum average neutron yield of (1±0.27)×104 n/shot for pure
D2 filling at 3 mbars was enhanced to (3.14±0.4)×105 n/shot with
D2+2% Kr admixture operation, which represents a >30-fold
increase. More than an order of magnitude enhancement in the
average neutron yield was observed over the broader operating
range of 1–4 mbars for D2+2% Kr and D2+5% Kr admixtures.
Order of magnitude enhancement in x-ray yield at low pressure deuteriumkrypton admixture operation in miniature plasma focus device
Verma, Rishi;
Lee, P.; Springham, S. V.; Tan, T. L.; Rawat, R. S.; Krishnan, M.;
National Institute of Education, Nanyang Technological University,, Singapore
Appl Phys Letts 2008 92 011506-011506-3
Abstract
In a 200 J fast miniature plasma focus device about 17- and 10-fold
increase in x-ray yield in spectral ranges of 0.9–1.6 keV and 3.2–
7.7 keV, respectively, have been obtained with deuterium-krypton
(D2–Kr) admixture at operating pressures of ≤0.4 mbar. In the
pressure range of ≫0.4–1.4 mbar, about twofold magnification in
average x-ray yield along with broadening of optimum pressure range
in both spectral ranges were obtained for D2–Kr admixtures. An order
of magnitude enhancement in x-ray yields at low pressures for
admixture operation will help in achieving high performance device
efficiency for lithography and micromachining applications.
3a. Proposed Mechanism
• Reduction of Sp Ht Ratio thus enhancing
compression
Kr Ionization
Kr thermodynamic data
% by volume 2% doping
Reduced Sp Ht Ratio of Kr-doped
deuterium is applied to Model Code
• Insufficient to explain order of magnitude
enhancement of SXR or NeutronsClaudia Tan, NTU thesis in progress
3b. Radiation Cooling and
Radiation Collapse
We now propose to look into radiation
cooling and radiation collapse as an
additional mechanism for the radiation
enhancement
Slow Compression Radiative Phase:
Piston Speed
In this phase the piston speed is:
 rp dI
1 rp dzf 4p g  1 rp dQ


drp
gI dt g  1 zf dt
gzf f c2 I 2 dt

g 1
dt
g
Here we have included energy loss/gain terms
into the equation of motion.
The plasma gains energy from Joule heating;
and loses energy through Bremsstrahlung & line radiation.
Energy term will tend to push the piston outwards.
Energy loss term will have the opposing effect.
Change C2 to CJ
where C1=1.6x10-40, C2=4.6x10-31, CJ=1300, b=/(8p2k)=1.2x1015
Threshold Current: Bremsstrahlung + Line
In PF operation, Line is predominant, so we leave out
recombination; Bremsstrahlung is included for comparison
Equation X
Third term RHS change C2 to CJ
For comparison Threshold current:
Bremsstrahlung only
• The Pease Braginskii current of 1.6 MA is obtained
by putting
• Joule Heating Rate=Bremsstrahlung Loss rate for
fully Ionized H (No line radiation); as follows:
where CJ=1300, C1=1.6x10-40, zeff=1, b=1.2x1015
Check: Pease-Braginskii Current is
where CJ=1300, C1=1.6x10-40, zeff=1, b=1.2x1015
Substituting the values, IP-B=1.6 MA
To show the relative effects of PBrems, PRec, PLine
& opposing PJoule for Xenon
Power factors-Pink :Lines Radiation; Blue:Recombination;
Oange:BremsStrahlung;
Red: Total Radiation; Black: Joule Heating (1 torr anode radius, a=1 cm)
Radiation Rate Factors
1.00E+09
Typical PF Operation left of arrow
1.00E+07
1.00E+05
1.00E+03
1.00E+01
1.00E-010.00
-1.00
1.00E-03
1.00
2.00
3.00
1.00E-05
1.00E-07
Log10 T in eV
4.00
5.00
6.00
For a more general case where line radiation is
predominant and hence has to be included: From
Equ X
Therefore:
The threshold current I which we may call the
line-radiation reduced P-B current I:
ie the line-radiation reduced P-B current is reduced by factor K1/2
Example of threshold current: Ar
• Argon at T=106K
• zeff=15.9
• K=1247
• K1/2=35
• and Ith=46kA
(not considering self absorption)
With self absorption, portion of radiation is not emitted
but self-absorped, the absorption adding to heating of
the plasma, increasing the Ith.
Example: Threshold current in Kr
• Kr at T=3*106K
• zeff=22
• K=1754
• K1/2=42
• and Ith=38kA
(not considering self absorption)
With self absorption, portion of radiation is not emitted
but self-absorped, the absorption adding to heating of
the plasma, increasing the Ith.
Radiative cooling and
Radiative Collapse
• Even in a small plasma focus operating in
argon or Kr, radiation collapse: for plasma
currents of even 50kA;
• plasma self-absorption will raise the
threshold current.
• Doped system will have also reduced Ith
• This is suggested as a mechanism for neutron
enhancement
Lee Model code includes power gain/loss
in its pinch dynamics
And the effect of plasma
self-absorption
• Plasma absorption correction factor:
Compensating for plasma self-absorption
• If no plasma self-absorption Aab =1.
• When Aab goes below 1, plasma self absorption
starts; and is incorporated; reducing emitted
radiation power
• When Aab reaches 1/e, plasma radiation switches
over from volume radiation to surface radiation
further reducing the emitted radiation power.
Configuring the Lee Model code for
the UNU ICTP PFF 3 kJ machine
Kr 0.1 Torr Joule power balances radiation power
• Compare computed with measured radial trajectory
Kr 0.5 Torr Joule power << radiation power
Kr 0.9 Torr Joule power << radiation power
Kr 1.1 Torr Joule power << radiation power
Kr 1.6 Torr Joule power << radiation power
Kr 1.7 Torr Joule power << radiation power
Kr 2 Torr Joule power << radiation power
Summary of trajectories
Strong Radiative Cooling leading to Radiative Collapse
(Model includes plasma self absorption)
0.1 Torr
0.5 Torr
0.4 Torr
0.9 Torr
Strong Radiative Cooling leading to Radiative Collapse
(Model includes plasma self absorption)
1.1 Torr
1.6 Torr
1.7 Torr
2 Torr
Conclusions from Numerical Experiments
• (1). Examine PF in Xe for production of EUV.
The low speeds required for optimum yield- PF may not be the
way to go for EUV.
• (2). Neutron yield enhancement in Kr-doped D: due to
thermodynamic effects of reduced Sp Ht Ratio?
Yield enhancement only partially due to reduced Sp Ht Ratio.
•
(3) Radiative cooling and radiative collapse of Kr focus pinch.
Lee Model code includes plasma self-absorption. In Kr
demonstrates radiative cooling leading to radiative collapse at
a pinch current ranging from 60-100 kA.
Thus radiative collapse effects could explain the observed yield
enhancement.
5th International Conference on the Frontiers
of Plasma Physics and Technology
18-22 April 2011, Singapore
MULTI-RADIATION MODELLING OF
THE PLASMA FOCUS
Sing Lee 1,2,3 and Sor Heoh Saw 1,2
1INTI
International University, 71800 Nilai, Malaysia
2Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia
3Nanyang Technological University, National Institute of Education, Singapore 637616
e-mails: ; [email protected]; [email protected]
Appendix: Sp Ht Ratio and a generalised
Sp Ht Ratio including radiation
 g=(f+2)/f
• Sp Ht ratio is a measure of degree of freedom
within a medium; f=3 ideal gas,
 g =5/3
• f= infinity g =1
 g is considered by aerodynamicists as an index of
compressibility e.g. shock-jump density ratio G=(g
+1)/(g -1) tends to infinity as g tends to 1; g tends to
1 is when f tends to infinity
Note how we may calculate the
effective degree of freedom of a plasma
2
 a r U r   a r U er 
f = 3+ m
( R o /M)TD
3 translational DF added to thermodynamic DF by computing
excitation and ionization energies per (1/2)kT per particle
Then using g =(2+f)/f, we express g as follows:
1

  a r U er 
g
5 m a rU r
= +
g -1 2
( R o /M)TD
Generalized Sp Ht Ratio
Express the radiative energy
as a degree of freedom
2
 a r U r   a r U er 
+radiative energy (Bremss + line)
f = 3+ m
( R o /M)TD
Hence find generalized SHR