1. Nuclear Fusion Energy- The role of the Plasma Focus
S Lee & S H Saw
Institute for Plasma Focus Studies
INTI International University, Malaysia
International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran

2. Outline of Talk Energy crisis Fusion Energy
The role of the Plasma Focus

3. Scenario: World Population stabilizes at 10 billion; consuming energy at 2/3 US 1985 per capita rate
Consumption
Shortfall
Supply
Fossil, Hydro, fission

4. Estimates of world energy production projected into the future in a scenario

5. Fusion Temperature attained Fusion confinement one step away
Needs x10 to reach ITER
Needs another 2x to reach Power Plant

6. Sizes of JET and ITER

8. Unlimited clean energy supply
no need to restrict
the growth of energy consumption,
a better standard of living or
the growth of population.
Man can choose
Figure 5: energy consumption into the 22nd century.
Such unlimited growth (curve 4 of Figure 5) need not imply unbridled wasteful consumption.
The best practice of environmental conservatism could be incorporated into growth, so that
efficient and ‘green’ habits become part of the sustained culture of the human race.

9. Figure 5: Scenario
Development of nuclear fusion energy is coming not a moment too soon.
The critical point when total available energy starts to decline is seen to be reached just before the middle of this century;
thereafter the consumption curve has to drop and
Man will have to cope with a decreasing supply
unless the increasing shortfall is made up by nuclear fusion energy

10. Large scale Fusion Experiments
Tokamaks: Low density, long confinement plasmas
Laser Implosions: Super-dense, sub-nanosecond plasmas
Smaller scale Fusion Experiments
Pinches: Dense, microsecond plasmas
Plasma Focus (PF) An advanced pinch system

11. Superior method for dense pinches
The Plasma Focus produces exceptional densities and temperatures.
A simple capacitor discharge is sufficient to power the plasma focus.

12. Plasma focus (PF)
Remarkably copious source of multiple radiations: x-rays, REBs, ions, plasma stream
Hence many applications
Fusion neutrons even in table top devices
Same energy density over 7 orders of magnitude of energy storage 0.1J to 1 MJ
Neutron Yield scaling established

13. THE PLASMA FOCUS (PF) The PF is divided into two sections.
Pre-pinch (axial) section: Delays the pinch until the capacitor discharge current approaches peak value.
The pinch starts & occurs at top of the current pulse.

14. Axial Accelaration Phase
The Plasma Dynamics in Focus
Radial Phase HV
30 mF, 15 kV
Axial Accelaration Phase
Inverse Pinch Phase

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

16. Dynamic Shock Wave process heats efficiently
However the dynamic process also has limitations; as we will see
Ultimately limits existing plasma focus in causing a yield scaling deterioration; as we shall see

17. 300J portable (25 kg); 106 neutrons per shot fusion device-at NTU-NIE

18. INTI UC Centre for Plasma Research -Plasma Focus & Pulse Power Laboratory
10 kV
2 Torr Neon
Current: 120 kA
Temperature:
2 million oC
Soft x-ray burst:
100 Megawatt-
10 ns
23 June First test shot of INTI-PF

19. 1997 ICDMP (International Centre for Dense Magnetised Plasmas) Warsaw-now operates one of biggest plasma focus in the world, the PF1000

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

21. Same Energy Density in small and big PF devices leads to:
Scalability
constant speed factor, [(I/a)/r1/2] for all machines, big or small lead to same plasma energy density
from 0.1 to 1000 kJ of storage energy
predictable yield of radiation
Constant speed factor also leads to constant dynamic resistance, which causes present generation PF’s to suffer scaling deterioration, or neutron saturation- more about this later

22. One of most exciting properties of plasma focus is its neutron yield Yn
Early experiments show: Yn~E02
Prospect was raised in those early research years that, breakeven could be attained at several tens of MJ .
However quickly shown that as E0 approaches 1 MJ, a neutron saturation effect was observed; Yn does not increase as much as expected, as E0 was progressively raised towards 1 MJ.
Question: Is there a fundamental reason for Yn saturation?

23. Chart from M Scholz (November 2007 ICDMP) purported to show neutron saturation

24. Global Scaling Law Scaling deterioration observed in numerical experiments (small black crosses) compared to measurements on various machines (larger coloured crosses) Neutron ‘saturation’ is more accurately portrayed as a scaling deterioration-Conclusion of IPFS-INTI UC research
S Lee & S H Saw, J Fusion Energy, (2008)
S Lee, Plasma Phys. Control. Fusion, 50 (2008)
S H Saw & S Lee. Scaling the plasma focus for fusion energy. Nuclear & Renewable Energy Sources Ankara, Turkey, 28 & 29 September 2009.
S Lee Appl Phys Lett 95, (2009)

25. At IPFS, we have shown that: constancy of axial phase dynamic resitance leads to current ‘saturation’ as E0 is increased by increasing C0. Tendency to saturate occurs before 1 MJ
From both numerical experiments as well as from accumulated laboratory data (D-D):
Yn= 3x1011Ipinch4.5
Yn= 2x1010Ipeak3.8
Hence the ‘saturation’ of Ipeak leads to saturation of neutron yield Yn

26. Scaling for large Plasma Focus
Targets:
IFMIF (International fusion materials irradiation facility)-level fusion wall materials testing

27. Fusion Wall materials testing at the mid-level of IFMIF: 1015 D-T neutrons per shot, 1 Hz, 1 year for dpa- Gribkov

28. Fast capacitor bank 10x PF1000-Fully modelled- 1
Fast capacitor bank 10x PF1000-Fully modelled- 1.5x1015 D-T neutrons per shot
Operating Parameters: 35kV, 14 Torr D-T
Bank Parameters: L0=33.5nH, C0=13320uF, r0=0.19mW
E0=8.2 MJ
Tube Parameters: b=35.1 cm, a=25.3 cm z0=220cm
Ipeak=7.3 MA, Ipinch=3.0 MA
Model parameters 0.13, 0.65, 0.35, 0.65

29. Ongoing IPFS numerical experiments of Multi-MJ Plasma Focus

30. 50 kV modelled- 1.2x1015 D-T neutrons per shot
Operating Parameters: 50kV, 40 Torr D-T
Bank Parameters: L0=33.5nH, C0=2000uF, r0=0.45mW
E0=2.5 MJ
Tube Parameters: b=20.9 cm, a=15 cm z0=70cm
Ipeak=6.7 MA, Ipinch=2.8 MA
Model parameters 0.14, 0.7, 0.35, 0.7

31. IFMIF-scale device
Numerical Experiments suggests the possibility of scaling the PF up to IFMIF mid-scale with a PF1000-like device at 50kV and 2.5 MJ at pinch current of 2.8MA

32. Scaling further- possibilities
1. Increase E0, however note: scaling deteriorated already below Yn~E0
2. Increase voltage, at 50 kV beam energy ~150kV already past fusion x-section peak; further increase in voltage, x-section decreases, so gain is marginal
Need technological advancement to increase current per unit E0 and per unit V0.
We next extrapolate from point of view of Ipinch

33. Scaling Plasma Focus from Ipinch using present predominantly beam-target in Lee Model code

34. 1. Using above Fig compute Pout at 1 Hz assume efficiency 0. 3 2
1.Using above Fig compute Pout at 1 Hz assume efficiency Then compute E0 budget to generate the required Ipinch at each point; so as to get Q=2

35. What we need for Focus fusion energy based on D-T
(note: 1 D-T neutron has 14.1 MeV of KE)
Choose 24 MA point from above graph:
Ipinch : MA
D-T n from scaling: 3x1019
Kinetic energy: MJ
Rep rate: shot per second
Then Pfusion (0.3 efficiency): MW
If E0=10MJ; input power at 1 Hz MW
Net Power MW
Technical Requirement: Ipinch= 24MA using E0=10MJ;
Rep rate required: 1 Hz

36. Thermonuclear Plasma Focus
Reason why PF fusion is beam-target is PF temp not high enough.
If use additional external heating from present 1 keV to 10 0r 20 keV, then Yth is dominant

37. Thermonuclear Plasma Focus

38. Thermonuclear fusion in PF with additional heating: Tech. Targets
Select a point from Fig 3 for discussion
10MA point at 20keV gives 3x10^19 D-T n /shot
This is equivalent to (Fig 1) b-t at 24 MA
At 1 Hz eff 0.3 (Fig 2) gives 20 MW
If require Q=2 (ie net power of 10 MW)
TechnologicalTargets: 4 MJ to generate 10MA
6 MJ to provide additional heating to 20keV

39. Plasma Focus Reactors Beam-target regime
improvement in technology is required:
to generate 24 MA pinch current from 10MJ at 30kV
Thermonuclear regime:
plasma focus operation;
with 10 MA from 3.5 MJ, no High voltage limit
then use additional heating (6 MJ budget) to reach 20 keV
Enhancement techniques:
Radiative collapse induced by Kr or Xe doping
Current injection using current-steps or beam injection

40. Radiative collapse increases number density
Yield proportional to n2, volume and duration
n2 ~ rmin-6
Volume x duration ~ rmin4
Thus yield ~ rmin-2; if compression increased 100 times, yield increases 10,000 times
Present radiative collapse involves hot spots containing only small proportion of pinch particles
Need gross (column) collapse

41. Thus radiative collapse is demonstrated in the numerical experiments
Pease & Braginskii postulated that D pinch may undergo radiative collapse at 1.6 MA (so-called P-B current) Krypton PF undergoes collapse much more easily, even below 105K, due to increased 1.thermodynamic degrees of freedom and 2. radiative degrees of freedom
Our model code includes thermodynamic effects and radiative effects coupled to the dynamics.
Thus radiative collapse is demonstrated in the numerical experiments

42. Numerical Experiments on 3 kJ PF demonstrating pinch column undergoing radiative collapse at optimum presssures
0.1 Torr
0.5 Torr
0.9 Torr
1.1 Torr

43. Small (3kJ) PF Pinch undergoing column radiative collapse at pinch currents as low as 80 kA

44. Kr- doped deuterium PF shows order of magnitude neutron yield enhancement
To learn to utilize this effect for large PF yield enhancment through radiative cooling and collapse

45. Conclusion:
Tokamak programme is moving steadily towards harnessing nuclear fusion energy as a limitless clean energy source for the continuing progress of civilisation
Alternative and smaller scale experiments will also play a role in this most challenging technological development – eg in neutron source at level of IFMIF
Scaling towards fusion reactor regimes is discussed; dependent upon technological advancement in production of larger currents from a budget of stored energy
Compression enhancement from radiative collapse of Kr-doped D-T PF also being experimented with numerically.

46. Nuclear Fusion Energy- The role of the Plasma Focus
S Lee & S H Saw
Institute for Plasma Focus Studies
INTI International University, Malaysia
International Workshop on Plasma Science & Applications, 27 & 28 October, Tehran, Iran