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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

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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
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
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.


The Plasma Focus Enhancement1/2

  • 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
Applications Enhancement

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
SXR lithography using EnhancementNX2 (Singapore) in Neon

16



Lines transferred using nx2 sxr
Lines transferred using NX2 SXR Enhancement

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

Modelled Mechanisms

Optimum Regime

Computed vs Measured


The plasma focus lee model code
The Plasma Focus and optimum regime–Lee Model code

Axial Phase Radial Phases


The 5 phases of lee model code
The 5-phases of Lee Model code and optimum regime

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
2. Modelling Xenon PF for EUV and optimum regime

  • 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 Z and optimum regimeeff for Temperature T, first calculate the ionization fractions, an (n=0 to 54) using Ionization Potential data from NIST


From the a n calculate z eff
From the and optimum regimean, calculate Zeff


Sp ht ratio g f 2 f
Sp Ht Ratio and optimum regimeg =(f+2)/f

  • Computation of f and g


Compute specific heat ratio g needed for calculating the radial dynamics
Compute Specific Heat Ratio and optimum regimeg needed for calculating the radial dynamics


To show the relative effects of p brems p rec p line opposing p joule for xenon
To show the relative effects of P and optimum regimeBrems, PRec, PLine& opposingPJouleforXenon

Typical PF Operation left of arrow


Conclusion for that work
Conclusion for that work and optimum regime

  • 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 and optimum regimeOrder 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 and optimum regime 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 200J fast miniature plasma focus device about 17- and 10-fold increase in x-ray yield in spectral ranges of 0.9–1.6keV and 3.2–7.7keV, respectively, have been obtained with deuterium-krypton (D2–Kr) admixture at operating pressures of ≤0.4mbar. In the pressure range of ≫0.4–1.4mbar, 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
3a. Proposed Mechanism and optimum regime

  • Reduction of Sp Ht Ratio thus enhancing compression


Kr ionization
Kr Ionization and optimum regime


Kr thermodynamic data
Kr thermodynamic data and optimum regime


By volume 2 doping
% by volume 2% doping and optimum regime


Reduced sp ht ratio of kr doped deuterium is applied to model code
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


3b radiation cooling and radiation collapse
3b. Radiation Cooling and Model CodeRadiation 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
Slow Compression Radiative Phase: Model Code Piston Speed


Where c 1 1 6x10 40 c 2 4 6x10 31 c j 1300 b m 8 p 2 k 1 2x10 15
where C Model Code1=1.6x10-40, C2=4.6x10-31, CJ=1300, b=m/(8p2k)=1.2x1015

Change C2 to CJ


Threshold Current: Bremsstrahlung + Line Model CodeIn 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
For comparison Threshold current: Bremsstrahlung only Model Code

  • 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
Check: Pease-Braginskii Current is Model Code

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 p brems p rec p line opposing p joule for xenon1
To show the relative effects of P Model CodeBrems, PRec, PLine& opposingPJouleforXenon

Typical PF Operation left of arrow


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


Therefore
Therefore: and hence has to be included: From


The threshold current i which we may call the line radiation reduced p b current i
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
Example of threshold current: Ar reduced P-B current I:

  • 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
Example: Threshold current in Kr reduced P-B current I:

  • 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
Radiative cooling and reduced P-B current I: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



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

  • Plasma absorption correction factor:


Compensating for plasma self absorption
Compensating for plasma self-absorption dynamics

  • 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.











Summary of trajectories machineStrong Radiative Cooling leading to Radiative Collapse(Model includes plasma self absorption)

0.1 Torr

0.4 Torr

0.5 Torr

0.9 Torr


Strong radiative cooling leading to radiative collapse model includes plasma self absorption
Strong Radiative Cooling leading to Radiative Collapse machine(Model includes plasma self absorption)

1.1 Torr

1.6 Torr

1.7 Torr

2 Torr


Conclusions from numerical experiments
Conclusions from Numerical Experiments machine

  • (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.


5 machineth 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
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
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:


Generalized sp ht ratio
Generalized Sp Ht Ratio a plasma

Express the radiative energy as a degree of freedom

Hence find generalized SHR

+radiative energy (Bremss + line)


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