1. MULTI-RADIATION MODELLING OF THE PLASMA FOCUS
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, Nilai, Malaysia
2Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia
3Nanyang Technological University, National Institute of Education, Singapore
s: ;

2. 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.

3. 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 Kr-doped Deuterium could at least in part be due to the enhanced compression caused by radiation cooling induced by the dopant.

4. The Plasma Focus /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

5. 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 nm
from industrial throughput considerations, output powers in excess of 1 kW (into 4p) 15

6. SXR lithography using NX2 (Singapore) in Neon16

7. Radial Compression (Pinch) Phase of the Plasma Focus

8. Lines transferred using NX2 SXR
X-ray masks in Ni & Au
SEM Pictures of transfers in AZPN114 using NX2 SXR 18

9. 1. Complementary modelling of NX2 SXR production mechanism and optimum regime
Modelled Mechanisms
Optimum Regime
Computed vs Measured

10. The Plasma Focus –Lee Model code
Axial Phase Radial Phases

11. 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

12. 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

14. Calculate Zeff for Temperature T, first calculate the ionization fractions, an (n=0 to 54) using Ionization Potential data from NIST

15. From the an, calculate Zeff

16. Sp Ht Ratio g =(f+2)/f
Computation of f and g

17. Compute Specific Heat Ratio g needed for calculating the radial dynamics

18. To show the relative effects of PBrems, PRec, PLine & opposing PJoule for Xenon
Typical PF Operation left of arrow

19. 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

20. 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, (2008); doi: / (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.

21. Order of magnitude enhancement in x-ray yield at low pressure deuterium-krypton 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
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.

22. 3a. Proposed Mechanism
Reduction of Sp Ht Ratio thus enhancing compression

23. Kr Ionization

24. Kr thermodynamic data

25. % by volume 2% doping

26. Reduced Sp Ht Ratio of Kr-doped deuterium is applied to Model Code
Insufficient to explain order of magnitude enhancement of SXR or Neutrons- Claudia Tan, NTU thesis in progress

27. 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

28. Slow Compression Radiative Phase: Piston Speed

29. where C1=1.6x10-40, C2=4.6x10-31, CJ=1300, b=m/(8p2k)=1.2x1015
Change C2 to CJ
where C1=1.6x10-40, C2=4.6x10-31, CJ=1300, b=m/(8p2k)=1.2x1015

30. 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

31. For comparison Threshold current: Bremsstrahlung only
The Pease Braginskii current of 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

32. 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

33. To show the relative effects of PBrems, PRec, PLine & opposing PJoule for Xenon
Typical PF Operation left of arrow

34. For a more general case where line radiation is predominant and hence has to be included: From Equ X

35. Therefore:

36. 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

37. 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.

38. 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.

39. 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

40. Lee Model code includes power gain/loss in its pinch dynamics

41. And the effect of plasma self-absorption
Plasma absorption correction factor:

42. 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.

43. Configuring the Lee Model code for the UNU ICTP PFF 3 kJ machine

44. Kr 0.1 Torr Joule power balances radiation power

45. Compare computed with measured radial trajectory

46. Kr 0.5 Torr Joule power << radiation power

47. Kr 0.9 Torr Joule power << radiation power

48. Kr 1.1 Torr Joule power << radiation power

49. Kr 1.6 Torr Joule power << radiation power

50. Kr 1.7 Torr Joule power << radiation power

51. Kr 2 Torr Joule power << radiation power

52. Summary of trajectories Strong Radiative Cooling leading to Radiative Collapse (Model includes plasma self absorption)
0.1 Torr
0.4 Torr
0.5 Torr
0.9 Torr

53. Strong Radiative Cooling leading to Radiative Collapse (Model includes plasma self absorption)
1.1 Torr
1.6 Torr
1.7 Torr
2 Torr

54. 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 kA.
Thus radiative collapse effects could explain the observed yield enhancement.

55. MULTI-RADIATION MODELLING OF THE PLASMA FOCUS
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, Nilai, Malaysia
2Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia
3Nanyang Technological University, National Institute of Education, Singapore
s: ;

56. 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

57. Note how we may calculate the effective degree of freedom of a plasma
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:

58. Generalized Sp Ht Ratio
Express the radiative energy as a degree of freedom
Hence find generalized SHR
+radiative energy (Bremss + line)