1. Plasma Focus- The Machine and
International School on Magnetohydrodynamics and Fusion Applications (ISMFA 2011) September 2011, ITAP, Turunc, Marmaris, Turkey
Plasma Focus- The Machine and
Scaling Properties
S H Saw and S Lee
INTI International University, Nilai, Malaysia
Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia

2. Plasma Focus- The Machine and Scaling Properties
Outline
Energy Storage in Plasma Focus spans 7 orders of magnitudes
How do properties scale?
1. Machine properties
- Ipeak, anode radius, storage energy
2. Axial phase scaling properties
- axial speed, speed factor, energy density
3. Radial phase scaling properties
-same speeds, temperatures, densities
hence same radiation intensities and
4. Radiation/particle yields depend only on
-pinched plasma dimensions, lifetimes

3. The Plasma Focus /2
Axial Phase Radial Phases

4. Scaling Properties 3 kJ machine Small Plasma Focus 1000 kJ machine
Big Plasma Focus

5. Comparison (Scaling) Important machine properties:
UNU ICTP PFF PF1000
E kJ at 15 kV kJ at 30kV
I kA 2MA
‘a’ cm cm

6. Comparison (Scaling) Important Compressed Plasma Properties
Density of plasma
Temperature of plasma
These two properties determine radiation intensity energy radiated per unit volume per unit lifetime of plasma)
Size of plasma
Lifetime of plasma
These two properties together with the above two determine total yield.

7. Experimental Observations of Temperatures and Densities PF1000
Anode length=56cm

8. PF1000: 60cm/7.7 us= 7.8 cm/us average speed End axial speed~ 12 cm/us

9. For PF1000; c~1.4 and speed ratio less than 2; our calculations show that radial speed~2x axial speed

10. Compare Temperatures UNU ICTP PFF PF1000
(from LS lecture) (this estimate)
Axial speed cm/us
Radial speed cm/us
Temperature x x K
Reflected S x x K After RS comes pinch phase which may increase T a little more in each case
Comparative T: about same; several million K

11. Compare Number Density
During shock propagation phase, density is controlled by the initial density and by the shock-’jump’ density
Shock density ratio=4 (for high T deuterium)
RS density ratio=3 times
On-axis density ratio=12
Initial at 3 torr n=2x1023 atoms m-3
RS density ni=2.4x1024 m-3 or 2.4x1018 per cc
Further compression at pinch; raises no. density higher typically to just under 1019 per cc.

12. Compare Number Density
Big or small PF initial density small range of several torr.
Similar shock processes
Similar final density

13. Big PF and small PF Same density, same temperature
Over a range of PFs smallest 0.1J to largest 1 MJ; over the remarkable range of 7 orders of magnitude- same initial pressure, same speeds
This leads to conclusion that all PF’s:
Same T, hence same energy (density) per unit mass
same n, hence same energy (density) per unit volume
Hence same radiation intensity

14. Next question: How does yield vary?
Yield is intensity x volume x lifetime
Dimensions and lifetime of the focus will determine radiation and particle yields.
How do dimensions and lifetime of compressed plasma vary from PF to PF?
Look at experimental observations

15. UNU ICTP PFF Radial inward shock phase & pinch Phase- ns shadowgraphy

16. PF1000: Nanosecond Imaging-laser shadowgraphs and high speed ns photography

17. Another set of PF1000 high speed imaging- framing and streak photography

18. Comparing large and small PF’s- Dimensions and lifetimes- putting shadowgraphs side-by-side, same scale
Lifetime ~10ns order of ~100 ns

19. Scaling properties-mainly axial phase 1/3
Comparing small (sub kJ) and large (thousand kJ) Plasma Focus Scaling Properties: size (energy) , current, speed and yield
Scaling properties-mainly axial phase /3

20. Scaling of anode radius ‘a’ with current (I) and storage energy (E0)
Scaling properties-machine properties
Peak current Ipeak increases with E0.
Anode radius ‘a’ increases with E0.
Current per cm of anode radius (ID) Ipeak /a : narrow range 160 to 210 kA/cm for all machines

21. Speeds, Speed Factor SF and Yn
Observed Peak axial speed va : 9 to 11 cm/us.
SF (speed factor) (Ipeak /a)/r0.5 :
narrow range 82 to 100 (kA/cm) per Torr 0.5 D
Fusion neutron yield Yn :
106 for PF400-J to 1011 for PF1000 (Yn 5 orders of magnitude for storage energy of 3 orders of magnitude)

22. Scaling properties-mainly radial phase 1/2
Comparing small (sub kJ) & large (thousand kJ) Plasma Focus Scaling Properties: size (‘a’) , T, pinch dimensions & duration
Scaling properties-mainly radial phase /2

23. Moreover number densities are also the same for big and small focus, in the pinsh compressed plasma around 1019/cc

24. Focus Pinch T, dimensions & lifetime with anode radius ‘a’
Scaling properties-mainly radial phase /2
Dimensions and lifetime scales as the anode radius ‘a’.
rmin/a (almost constant at )
zmax/a (almost constant at 1.5)
Pinch duration narrow range 8-14 ns/cm of ‘a’
Tpinch is measure of energy per unit mass.
Quite remarkable that this energy density varies so little (factor of 5) over such a large range of device energy (factor of 1000).

25. Scaling Properties: Pinch Dimensions & Duration: Compare D & Ne
(Lee, Kudowa 1998, Cairo 2003)

26. Rule-of-thumb scaling properties, (subject to minor variations caused primarily by the variation in c=b/a) over whole range of device
Axial phase energy density (per unit mass) constant
Radial phase energy density (per unit mass) constant
Pinch radius ratio constant
Pinch length ratio constant
Pinch duration per unit anode radius constant

27. Further equivalent Scaling Properties
Constant axial phase energy density (Speed Factor (I/a)/r0.5, speed) equivalent to constant dynamic resistance
I/a approx constant since r has only a relatively small range for each gas
Also strong relationship requirement between plasma transit time and capacitor time t0= (L0C0)0.5
E.g. strong interaction between t0 and ‘a’ and I for a given bank.

28. Energy Storage in Plasma Focus spans 7 orders of magnitudes
Conclusion
Energy Storage in Plasma Focus spans 7 orders of magnitudes
We discussed the scaling of properties
1. Machine properties
- Ipeak, anode radius ‘a’, storage energy; (Ipeak/a)=constant
2. Axial phase scaling properties
- axial speed, speed factor, energy density; constant
3. Radial phase scaling properties
-same speeds, temperatures, densities; constant
hence same radiation intensities and
4. Radiation/particle yields depend only on
-pinched plasma dimensions, lifetimes: depend on ‘a’, on I
The current dominates Plasma Focus Yields

29. Plasma Focus- The Machine and
International School on Magnetohydrodynamics and Fusion Applications (ISMFA 2011) September 2011, ITAP, Turunc, Marmaris, Turkey
Plasma Focus- The Machine and
Scaling Properties
S H Saw and S Lee
INTI International University, Nilai, Malaysia
Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia