1. 5 th 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 1 INTI International University, 71800 Nilai, Malaysia 2 Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia 3 Nanyang Technological University, National Institute of Education, Singapore 637616 e-mails: ; leesing@optusnet.com.au; sorheoh.saw@newinti.edu.my leesing@optusnet.com.ausorheoh.saw@newinti.edu.my

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 I P-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 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

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 0.8-1.4 nm –from industrial throughput considerations, output powers in excess of 1 kW (into 4  ) 15

6. SXR lithography using NX2 (Singapore) in Neon 16

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

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

13. 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

15. Calculate Z eff for Temperature T, first calculate the ionization fractions,  n (n=0 to 54) using Ionization Potential data from NIST

16. From the  n, calculate Z eff

17. Sp Ht Ratio  =(f+2)/f Computation of f and 

18. Compute Specific Heat Ratio  needed for calculating the radial dynamics

19. To show the relative effects of P Brems, P Rec, P Line & opposing P Joule for Xenon Typical PF Operation left of arrow

20. 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

21. 3. Kr-doped Deuterium Order of magnitude enhancement in neutron emission with deuterium-krypton admixture in miniature plasma focus device Rishi Verma 1, P Lee 1, S Lee 1, S V Springham 1, T L Tan 1, R S Rawat 1, M. Krishnan 2 1 National Institute of Education, Nanyang Technological University, Singapore 2 Alameda 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)×10 4 n/shot for pure D2 filling at 3 mbars was enhanced to (3.14±0.4)×10 5 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.

22. 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 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.

23. 3a. Proposed Mechanism Reduction of Sp Ht Ratio thus enhancing compression

24. Kr Ionization

25. Kr thermodynamic data

26. % by volume 2% doping

27. 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

28. 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

29. Slow Compression Radiative Phase: Piston Speed

30. where C 1 =1.6x10 -40, C 2 =4.6x10 -31, C J =1300, b=  /(8  2 k)=1.2x10 15 Change C 2 to C J

31. Threshold Current: Bremsstrahlung + Line In PF operation, Line is predominant, so we leave out recombination; Bremsstrahlung is included for comparison Third term RHS change C 2 to C J Equation X

32. 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 C J =1300, C 1 =1.6x10 -40, z eff =1, b=1.2x10 15

33. Check: Pease-Braginskii Current is where C J =1300, C 1 =1.6x10 -40, z eff =1, b=1.2x10 15 Substituting the values, I P-B =1.6 MA

34. To show the relative effects of P Brems, P Rec, P Line & opposing P Joule for Xenon Typical PF Operation left of arrow

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

36. Therefore:

37. 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 K 1/2

38. Example of threshold current: Ar Argon at T=10 6 K z eff =15.9 K=1247 K 1/2 =35 and I th =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 I th.

39. Example: Threshold current in Kr Kr at T=3*10 6 K z eff =22 K=1754 K 1/2 =42 and I th =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 I th.

40. 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 I th This is suggested as a mechanism for neutron enhancement

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

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

43. Compensating for plasma self-absorption If no plasma self-absorption A ab =1. When A ab goes below 1, plasma self absorption starts; and is incorporated; reducing emitted radiation power When A ab reaches 1/e, plasma radiation switches over from volume radiation to surface radiation further reducing the emitted radiation power.

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

45. Kr 0.1 Torr Joule power balances radiation power

46. Compare computed with measured radial trajectory

47. Kr 0.5 Torr Joule power << radiation power

48. Kr 0.9 Torr Joule power << radiation power

49. Kr 1.1 Torr Joule power << radiation power

50. Kr 1.6 Torr Joule power << radiation power

51. Kr 1.7 Torr Joule power << radiation power

52. Kr 2 Torr Joule power << radiation power

53. Summary of trajectories Strong Radiative Cooling leading to Radiative Collapse (Model includes plasma self absorption) 0.1 Torr0.4 Torr 0.5 Torr0.9 Torr

54. Strong Radiative Cooling leading to Radiative Collapse (Model includes plasma self absorption) 1.1 Torr 1.6 Torr 1.7 Torr2 Torr

55. 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.

56. 5 th 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 1 INTI International University, 71800 Nilai, Malaysia 2 Institute for Plasma Focus Studies, 32 Oakpark Drive, Chadstone, VIC 3148, Australia 3 Nanyang Technological University, National Institute of Education, Singapore 637616 e-mails: ; leesing@optusnet.com.au; sorheoh.saw@newinti.edu.my leesing@optusnet.com.ausorheoh.saw@newinti.edu.my

57. Appendix: Sp Ht Ratio and a generalised Sp Ht Ratio including radiation =(f+2)/f Sp Ht ratio is a measure of degree of freedom within a medium; f=3 ideal gas,  =5/3 f=infinity  =1  is considered by aerodynamicists as an index of compressibility e.g. shock-jump density ratio  =(  +1)/(  -1) tends to infinity as  tends to 1;  tends to 1 is when f tends to infinity

58. 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  =(2+f)/f, we express g as follows:

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