55thth International Conference on the Frontiers International Conference on the Frontiers of Plasma Physics and Technologyof Plasma Physics and Technology

18-22 April 2011, Singapore18-22 April 2011, Singapore

MULTI-RADIATION MODELLING OF MULTI-RADIATION MODELLING OF THE PLASMA FOCUSTHE 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, Australia3Nanyang Technological University, National Institute of Education, Singapore 637616

e-mails: ; leesing@optusnet.com.au; sorheoh.saw@newinti.edu.my

Outline of Talk-Applications of Plasma Outline of Talk-Applications of Plasma Focus RadiationFocus 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 Outline of Talk: Role of Radiation Cooling for Neutron Yield EnhancementNeutron 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.

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

ApplicationsApplications

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

SXR lithography using SXR lithography using NX2 (Singapore) in NeonNX2 (Singapore) in Neon

8 9 10 11 12 13 140.0

0.2

0.4

0.6

0.8

1.0

ba

9 8

2

34

567

1

inten

sity

(a.u.

)

wavelength (Å)

16

Radial Compression (Pinch) Radial Compression (Pinch) Phase of the Plasma FocusPhase of the Plasma Focus

Lines transferred using NX2 SXRLines transferred using NX2 SXR

SEM Pictures of transfers in AZPN114 using NX2 SXR

X-ray masks in Ni & Au

18

1. Complementary modelling of NX2 SXR 1. Complementary modelling of NX2 SXR production mechanism and optimum regimeproduction mechanism and optimum regime

Modelled Mechanisms

Optimum Regime

Computed vs Measured

The Plasma FocusThe Plasma Focus –Lee Model code–Lee Model code

Axial Phase Radial Phases

The 5-phases of Lee Model codeThe 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 EUV2. 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 ZCalculate Zeffeff for Temperature T, first calculate for Temperature T, first calculate the ionization fractions, the ionization fractions, nn (n=0 to 54) using (n=0 to 54) using

Ionization Potential data from NISTIonization Potential data from NIST

Xenon ionization Fractions Corona Model

0

0.2

0.4

0.6

0.8

1

-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Log(10) of T in eV

Ioni

zatio

n Fr

actio

ns

From the From the nn, calculate Z, calculate Zeffeff

Zeff of Xenon Corona Model

0

10

20

30

40

50

0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00

Log(10) of T in eV

Zef

f

Sp Ht Ratio Sp Ht Ratio =(f+2)/f =(f+2)/f• Computation of f and

/M)TDR(

U U m +

2

5 =

- o

errrr

1

1

/M)TDR(

UU m

2

+ 3 = fo

errrr

Compute Specific Heat Ratio Compute Specific Heat Ratio needed for needed for calculating the radial dynamicscalculating the radial dynamics

Specific Heat Ratio Xenon

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

-1.00 1.00 3.00 5.00 7.00

Log(10) of T in eV

To show the relative effects of PTo show the relative effects of PBremsBrems, P, PRecRec, P, PLineLine

& opposing& opposing PPJouleJoule forfor XenonXenonPower factors-Pink :Lines Radiation; Blue:Recombination;

Oange:BremsStrahlung; Red: Total Radiation; Black: Joule Heating (1 torr anode radius, a=1 cm)

1.00E-07

1.00E-05

1.00E-03

1.00E-01

1.00E+01

1.00E+03

1.00E+05

1.00E+07

1.00E+09

-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

Log10 T in eV

Rad

iatio

n R

ate

Fac

tors

Typical PF Operation left of arrow

Conclusion for that workConclusion 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 Deuterium3. Kr-doped DeuteriumOrder of magnitude enhancementOrder of magnitude enhancement in in neutron emissionneutron emission with with

deuterium-krypton admixture in miniature plasma focus devicedeuterium-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 enhancementOrder of magnitude enhancement in in x-ray yieldx-ray yield at low pressure deuterium- at low pressure deuterium-krypton admixture operation in miniature plasma focus devicekrypton 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 011506-011506-3Abstract

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 Mechanism3a. Proposed Mechanism

• Reduction of Sp Ht Ratio thus enhancing compression

Kr IonizationKr Ionization

Kr thermodynamic dataKr thermodynamic data

% by volume 2% doping% by volume 2% doping

Reduced Sp Ht Ratio of Kr-doped Reduced Sp Ht Ratio of Kr-doped deuterium is applied to Model deuterium is applied to Model

CodeCode

• Insufficient to explain order of magnitude enhancement of SXR or Neutrons- Claudia Tan, NTU thesis in progress

3b. Radiation Cooling and 3b. Radiation Cooling and Radiation CollapseRadiation Collapse

We now propose to look into radiation cooling and radiation collapse as an additional mechanism for the radiation enhancement

Slow Compression Radiative Phase: Slow Compression Radiative Phase: Piston Speed Piston Speed

1

f14

dt11

22cf

f

f

dtdQ

I

r

zdz

z

r

dtdI

I

r

dt

drppp

p

In this phase the piston speed is:

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.

where Cwhere C11=1.6x10=1.6x10-40-40, C, C22=4.6x10=4.6x10-31-31, C, CJJ=1300, b==1300, b=/(8/(822k)=1.2x10k)=1.2x101515

Change C2 to CJ

Threshold Current: Bremsstrahlung + LineThreshold Current: Bremsstrahlung + Line In PF operation, Line is predominant, so we leave out In PF operation, Line is predominant, so we leave out

recombination; Bremsstrahlung is included for comparisonrecombination; Bremsstrahlung is included for comparison

Third term RHS change C2 to CJEquation X

For comparison Threshold current: For comparison Threshold current: Bremsstrahlung onlyBremsstrahlung 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 isCheck: 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 PTo show the relative effects of PBremsBrems, P, PRecRec, P, PLineLine

& opposing& opposing PPJouleJoule forfor XenonXenonPower factors-Pink :Lines Radiation; Blue:Recombination;

Oange:BremsStrahlung; Red: Total Radiation; Black: Joule Heating (1 torr anode radius, a=1 cm)

1.00E-07

1.00E-05

1.00E-03

1.00E-01

1.00E+01

1.00E+03

1.00E+05

1.00E+07

1.00E+09

-1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00

Log10 T in eV

Rad

iatio

n R

ate

Fac

tors

Typical PF Operation left of arrow

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

Equ XEqu X

Therefore:Therefore:

The threshold current I which we may call the The threshold current I which we may call the line-radiation reduced P-B current I: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: ArExample 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 KrExample: 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 cooling and Radiative CollapseRadiative 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 Lee Model code includes power gain/loss in its pinch dynamicsin its pinch dynamics

And the effect of plasma And the effect of plasma self-absorptionself-absorption

• Plasma absorption correction factor:

Compensating for plasma self-absorptionCompensating 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 Configuring the Lee Model code for the UNU ICTP PFF 3 kJ machinethe UNU ICTP PFF 3 kJ machine

Kr 0.1 Torr Joule power balances radiation powerKr 0.1 Torr Joule power balances radiation power

• Compare computed with measured radial trajectory

Kr 0.5 Torr Joule power << radiation powerKr 0.5 Torr Joule power << radiation power

Kr 0.9 Torr Joule power << radiation powerKr 0.9 Torr Joule power << radiation power

Kr 1.1 Torr Joule power << radiation powerKr 1.1 Torr Joule power << radiation power

Kr 1.6 Torr Joule power << radiation powerKr 1.6 Torr Joule power << radiation power

Kr 1.7 Torr Joule power << radiation powerKr 1.7 Torr Joule power << radiation power

Kr 2 Torr Joule power << radiation powerKr 2 Torr Joule power << radiation power

Summary of trajectoriesSummary of trajectoriesStrong Radiative Cooling leading to Radiative CollapseStrong Radiative Cooling leading to Radiative Collapse

((Model includes plasma self absorption)Model includes plasma self absorption)

0.1 Torr 0.4 Torr

0.5 Torr 0.9 Torr

Strong Radiative Cooling leading to Radiative CollapseStrong Radiative Cooling leading to Radiative Collapse((Model includes plasma self absorption)Model includes plasma self absorption)

1.1 Torr

1.6 Torr

1.7 Torr 2 Torr

Conclusions from Numerical ExperimentsConclusions 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.

55thth International Conference on the Frontiers International Conference on the Frontiers of Plasma Physics and Technologyof Plasma Physics and Technology

18-22 April 2011, Singapore18-22 April 2011, Singapore

MULTI-RADIATION MODELLING OF MULTI-RADIATION MODELLING OF THE PLASMA FOCUSTHE 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, Australia3Nanyang Technological University, National Institute of Education, Singapore 637616

e-mails: ; leesing@optusnet.com.au; sorheoh.saw@newinti.edu.my

Appendix: Sp Ht Ratio and a generalised Appendix: Sp Ht Ratio and a generalised Sp Ht Ratio including radiationSp 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

Note how we may calculate the Note how we may calculate the effective degree of freedom of a plasmaeffective degree of freedom of a plasma

/M)TDR(

UU m

2

+ 3 = fo

errrr

/M)TDR(

U U m +

2

5 =

- o

errrr

1

1

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:

Generalized Sp Ht RatioGeneralized Sp Ht RatioExpress the radiative energy

as a degree of freedom

Hence find generalized SHR

/M)TDR(

UU m

2

+ 3 = fo

errrr +radiative energy (Bremss + line)