Seminar on Plasma Focus Experiments SPFE2010 Use of current measurements to interpret plasma focus properties and mechanisms S Lee, S H Saw INTI International.

Seminar on Plasma Focus Experiments Seminar on Plasma Focus Experiments SPFE2010SPFE2010

Use of current measurements to interpret Use of current measurements to interpret plasma focus properties and mechanismsplasma focus properties and mechanisms

S Lee, S H SawS Lee, S H SawINTI International University, Nilai, MalaysiaINTI International University, Nilai, Malaysia

Institute for Plasma Focus Studies, Melbourne, Malaysia, SingaporeInstitute for Plasma Focus Studies, Melbourne, Malaysia, Singapore

Nanyang Technological University, NIE, SingaporeNanyang Technological University, NIE, Singapore

OutlineOutline

The Lee model code and its contributions to The Lee model code and its contributions to landmark plasma focus understandinglandmark plasma focus understanding

Use of the code to reference diagnosticsUse of the code to reference diagnostics Current waveforms show necessity to classify Current waveforms show necessity to classify

PF’s into T1 and T2PF’s into T1 and T2 T2 shows necessity to model 6T2 shows necessity to model 6 thth phase ie Phase phase ie Phase

4a4a Product of this fitting is the magnitude and Product of this fitting is the magnitude and

temporal form of anomalous resistance.temporal form of anomalous resistance.

Insights 1/3Insights 1/3

The Lee model code has produced The Lee model code has produced ground-breaking insights no other ground-breaking insights no other plasma focus codes has been able to plasma focus codes has been able to produceproduce

For Example: Ground-breaking For Example: Ground-breaking Insights published 2/3Insights published 2/3

Limitation to Pinch Current and Yields-Limitation to Pinch Current and Yields- Appl Phys Letts. 92 Appl Phys Letts. 92 (2008) S Lee & S H Saw: (2008) S Lee & S H Saw: an unexpected, important resultan unexpected, important result

Neutron Yield Scaling-sub kJ to 1 MJNeutron Yield Scaling-sub kJ to 1 MJ--J Fusion Energy 27 (2008) J Fusion Energy 27 (2008)

S Lee & S H Saw- S Lee & S H Saw- multi-MJmulti-MJ- - PPCF 50 (2008) S LeePPCF 50 (2008) S Lee

Neon Soft x-ray Scaling-Neon Soft x-ray Scaling- PPCF 51 (2009) S Lee, S H Saw, P Lee, R S PPCF 51 (2009) S Lee, S H Saw, P Lee, R S RawatRawat

Neutron Yield Saturation- Neutron Yield Saturation- Appl Phys Letts. 95 (2009) S LeeAppl Phys Letts. 95 (2009) S Lee simple explanation of major obstruction to progress for a generationsimple explanation of major obstruction to progress for a generation

Others papers we published using the Others papers we published using the Lee model code numerical experiments Lee model code numerical experiments

3/33/3Techniques: of Pinch current from total Techniques: of Pinch current from total

current measurements, in-situ current measurements, in-situ determination of bank parameters determination of bank parameters

(2 papers 2008, 2010) ; (2 papers 2008, 2010) ;

numerical experiments applied to numerical experiments applied to specific machines (3 papers 2009); specific machines (3 papers 2009);

soft x-rays from nitrogen and oxygen soft x-rays from nitrogen and oxygen

(4 papers with Syrian AEC 2009, 2010)(4 papers with Syrian AEC 2009, 2010)

The 5-phase Lee Model code 1/4The 5-phase Lee Model code 1/4

Includes electrodynamical- and radiation- Includes electrodynamical- and radiation- coupled equations to portray the REGULAR coupled equations to portray the REGULAR mechanisms of the axial (phase 1), radial mechanisms of the axial (phase 1), radial inward shock (phase 2), radial RS (phase 3), inward shock (phase 2), radial RS (phase 3), slow compression radiation phase (phase 4) & slow compression radiation phase (phase 4) & the expanded axial post-pinch phase (phase 5)the expanded axial post-pinch phase (phase 5)

Relates to physical reality through a measured Relates to physical reality through a measured current tracecurrent trace

Given any plasma focus machine: e.g. Given any plasma focus machine: e.g. PF1000 (biggest PF in the world) 2/4PF1000 (biggest PF in the world) 2/4

Bank parameters: L0=33nH; C0=1332uF; r0=6 mwBank parameters: L0=33nH; C0=1332uF; r0=6 mw Tube parameters: b=16 cm, a=11.55 cm, z0=60cmTube parameters: b=16 cm, a=11.55 cm, z0=60cm Operation parameters: V0=27kV, P0=3.5 Torr in D2Operation parameters: V0=27kV, P0=3.5 Torr in D2

The UPFLF (Lee code) is configuredThe UPFLF (Lee code) is configured (by keying figures into the configuration (by keying figures into the configuration panel on the EXCEL sheet) as the PF1000panel on the EXCEL sheet) as the PF1000

Output of codeOutput of code: PF1000 current waveform: PF1000 current waveform

PF1000 dynamics & electrodynamicsPF1000 dynamics & electrodynamics

PF1000 plasma pinch dimensions & characteristicsPF1000 plasma pinch dimensions & characteristics

PF1000 neutron & Radiation yieldsPF1000 neutron & Radiation yields

1997 ICDMP 1997 ICDMP (International Centre for Dense Magnetised (International Centre for Dense Magnetised

Plasmas)Plasmas) established in Warsaw-now operates one established in Warsaw-now operates one of biggest plasma focus in the world, the PF1000of biggest plasma focus in the world, the PF1000

Connection of model with Reality is by means of Connection of model with Reality is by means of a measured current waveform 3/4a measured current waveform 3/4

The computed current waveform is fitted to the measured current The computed current waveform is fitted to the measured current

waveform by adjusting 4 physical parameters:waveform by adjusting 4 physical parameters: ffmm && f fcc: mass swept up & current factor; axial phase: mass swept up & current factor; axial phase ffmrmr && f fcrcr: : mass swept up & current factorsmass swept up & current factors: radial phase: radial phase

5-point fit: rising slope, topping profile, peak value, slope of dip, depth of dip

Once fitted: model is energy-wise & mass-wise Once fitted: model is energy-wise & mass-wise & equivalent to the physical situation 4/4& equivalent to the physical situation 4/4

All dynamics, electrodynamics, radiation, All dynamics, electrodynamics, radiation, plasma properties and neutron yields are plasma properties and neutron yields are realistically simulated; so that the code output realistically simulated; so that the code output of these quantities may be used as reference of these quantities may be used as reference points for diagnosticspoints for diagnostics

Diagnostics-Time histories of dynamics, energies and Diagnostics-Time histories of dynamics, energies and plasma properties computed by the codeplasma properties computed by the code

Last adjustment, when the computed Last adjustment, when the computed IItotaltotal trace is judged to be reasonably well fitted in all 5 features, computed times trace is judged to be reasonably well fitted in all 5 features, computed times histories are presented (NX2 operated at 11 kV, 2.6 Torr neon)histories are presented (NX2 operated at 11 kV, 2.6 Torr neon)

Computed Itotal waveform fitted to measuredComputed Itotal waveform fitted to measured

Computed Tube voltageComputed Tube voltage

Computed Itotal & IplasmaComputed Itotal & Iplasma

Computed axial trajectory & speedComputed axial trajectory & speed

Input: Measured Total Current; shown with fitted computed total current

0

50

100

150

200

250

300

350

400

0 0.5 1 1.5 2 2.5Time in microsec

Cu

rren

t in

kA

Measured currentkAComputed currentkA

end of radial phase

Computed Tube Voltage

-5

0

5

10

15

20

25

0.0 0.5 1.0 1.5 2.0 2.5

Time in microsec

Vo

ltag

e in

kV Breech Voltage kV

Computed Total Current & Plasma Current

0

50

100

150

200

250

300

350

400

0.0 0.5 1.0 1.5 2.0 2.5

Time in microsec

Cu

rren

t in

kA

Total Current kA

Plasma Current

Computed Axial Trajectory & Speed

0

2

4

6

8

10

12

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

Pos

ition

in c

m,

S

peed

in c

m/u

sec

Axial positionAxial Speed

Computed tube Inductance (axial + radial)

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

Ind

uct

ance

in n

H

Plasma Inductance

Computed total inductive energy as % of stored energy

010

2030

4050

6070

80

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

% o

f st

ore

d e

ner

gy

Inductive energy

Compare energy dissipated by 'dynamic resistance' with piston work

0

5

10

15

20

25

30

35

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

% o

f st

ore

d e

ner

gy

energy dissipated by 0.5LdotPiston Work

Dynamic Resistance in mOhm

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

DR

in m

Ohm

DR in mOhm

Computed Radial trajectory, Shock & Reflected Shock

-5

0

5

10

15

20

0.0 0.5 1.0 1.5 2.0 2.5

Time in microsec

Ra

dia

l po

sit

ion

in m

m

Radial Inward Shock

Radial Piston

Radial Reflected Shock

Computed Length of Radial Structure

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5

Time in microsec

Leng

th in

mm

Length of Radial Structure

Computed Radial speeds, Shock, Reflected Shock & elongation

-30

-20

-10

0

10

20

30

0 1 1 2 2 3

Time in microsec

Sp

eed

s in

cm

/use

c

Radial Inw ard Shock

Radial Piston

Elongation Speed

Computed averaged and peak plasma temperature

0.0

1.0

2.0

3.0

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

Tem

p (

106

K)

Averaged uniform T

Peak (temporal & spatial) T

Computed averaged & peak ion number density

0

5

10

15

20

25

30

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

nu

mb

er d

ensi

ty 1

023

m-3

Averaged uniform ni

nimax, full shock jump

Computed SXR Power in GW

0.0

1.0

2.0

3.0

0.0 0.5 1.0 1.5 2.0 2.5Time in microsec

SX

R P

ower

in G

W

SXR emission power

piston

All well-published PF machines are well-fittedAll well-published PF machines are well-fitted: see : see following examples and many others; following examples and many others;

note: note: the fit for the axial phase, and for the radial phasethe fit for the axial phase, and for the radial phase 1/4 1/4

ExceptExcept one 2/4 one 2/4 UNU ICTP PFF- famed low-cost sharing network; UNU ICTP PFF- famed low-cost sharing network;

current signal noisy and dip is small; difficult to current signal noisy and dip is small; difficult to judge the fitting-suspected ill-fitjudge the fitting-suspected ill-fit

Low cost- necessitates single capacitor- hence high Low cost- necessitates single capacitor- hence high inductance Linductance L00

Recently KSU commissioned a machine; a Recently KSU commissioned a machine; a modernised version of the UNU ICTP PFF 3/4modernised version of the UNU ICTP PFF 3/4

A good Rogowski system was developed to measure A good Rogowski system was developed to measure dI/dt; which was then numerically integrated resulting in a dI/dt; which was then numerically integrated resulting in a clean current signal-clean current signal-

Best fit nowhere near the fit of the well-published machines- in fact Best fit nowhere near the fit of the well-published machines- in fact clearly could only fit a small portion of the radial phaseclearly could only fit a small portion of the radial phase

A study followed; resulting in classifying plasma A study followed; resulting in classifying plasma focus devices into T1 & T2 4/4focus devices into T1 & T2 4/4

Differentiator: L0

Better Differentiators: RL=(L0 +La)/Lp

REL=(EL0+ELa)/ELPinch

Physical explanation 1/2Physical explanation 1/2

RD mechanism for pinch purely compressiveRD mechanism for pinch purely compressive At end of RD (call this REGULAR DIP), expts At end of RD (call this REGULAR DIP), expts

show other effects eg instabilities leading to show other effects eg instabilities leading to anomalous resistance- these mechanisms not anomalous resistance- these mechanisms not modelled by 5-phase Lee codemodelled by 5-phase Lee code

These anomalous resistive effects will absorb These anomalous resistive effects will absorb further energy from pinch; will result in further further energy from pinch; will result in further current dips- called EXTENDED DIP, EDcurrent dips- called EXTENDED DIP, ED

Our studies further concluded 2/2Our studies further concluded 2/2

T1: Small LT1: Small L0 0 lead to big RD and relatively small EDlead to big RD and relatively small ED T2: Big LT2: Big L00 lead to small RD and relatively big ED lead to small RD and relatively big ED

This explains why the 5-phase model: This explains why the 5-phase model:

For T1: the model parameters can be stretched for the For T1: the model parameters can be stretched for the RD to ‘absorb’ the EDRD to ‘absorb’ the ED

For T2: the model parameters, stretch how one likes, the For T2: the model parameters, stretch how one likes, the RD cannot ‘absorb’ the EDRD cannot ‘absorb’ the ED

Need to develop 6Need to develop 6thth phase ie Phase phase ie Phase 4a 1/24a 1/2

We have simulated using anomalous We have simulated using anomalous resistance of following form:resistance of following form:

Where R0 is of order of 1 Ohm, t1 controls Where R0 is of order of 1 Ohm, t1 controls rise time of the anomalous resistance rise time of the anomalous resistance and t2 controls the fall time (rate)and t2 controls the fall time (rate)

Use one term to fit one feature; terminate the Use one term to fit one feature; terminate the termterm

Then use a 2nd term to fit a 2Then use a 2nd term to fit a 2ndnd feature and so feature and so onon

Simulated Anomalous Resistance Term 2/2Simulated Anomalous Resistance Term 2/2

Result of Phase 4a fitting applied to Result of Phase 4a fitting applied to KSU Current Trace 1/3KSU Current Trace 1/3

2/32/3

Features 3/3Features 3/3 Current ED now fitted very wellCurrent ED now fitted very well Fig also shows the form of the fitted anomalous resistance Fig also shows the form of the fitted anomalous resistance

(3 terms)(3 terms) Figure shows that the computed tube voltage waveform Figure shows that the computed tube voltage waveform

also shows features in agreement with the measured tube also shows features in agreement with the measured tube voltage waveformvoltage waveform

The product of this Phase 4a fitting is the magnitude and The product of this Phase 4a fitting is the magnitude and temporal form of the anomalous resistance. This is an temporal form of the anomalous resistance. This is an important experimental result. The information is useful to important experimental result. The information is useful to elaborate further on the instability mechanisms. elaborate further on the instability mechanisms.

Moreover even for the T1 current waveforms, we should Moreover even for the T1 current waveforms, we should fit by first just fitting the RD using the 5-phase model; ie fit by first just fitting the RD using the 5-phase model; ie the part that fits well with the computed is the RD; the rest the part that fits well with the computed is the RD; the rest of the dip os then fitted using phase 4a.of the dip os then fitted using phase 4a.

ConclusionConclusionIn this paper we have discussed:In this paper we have discussed:

The Lee model code and its contributions The Lee model code and its contributions to landmark plasma focus understandingto landmark plasma focus understanding

Use of the code to reference diagnosticsUse of the code to reference diagnostics Current waveforms show necessity to Current waveforms show necessity to

classify PF’s into T1 and T2classify PF’s into T1 and T2 T2 shows necessity to model 6T2 shows necessity to model 6thth phase ie phase ie

Phase 4aPhase 4a Product of this fitting is the magnitude Product of this fitting is the magnitude

and temporal form of anomalous and temporal form of anomalous resistance.resistance.

A Paper has been submitted:A Paper has been submitted:

Use of current measurements to interpret plasma Use of current measurements to interpret plasma focus properties and mechanismsfocus properties and mechanisms

S Lee, S H SawS Lee, S H SawINTI International University, Nilai, MalaysiaINTI International University, Nilai, Malaysia

Institute for Plasma Focus Studies, Melbourne, Malaysia, SingaporeInstitute for Plasma Focus Studies, Melbourne, Malaysia, Singapore

Nanyang Technological University, NIE, SingaporeNanyang Technological University, NIE, Singapore