Plasma Focus- The Machine and International School on Magnetohydrodynamics and Fusion Applications (ISMFA 2011) 9-17 September 2011, ITAP, Turunc, Marmaris, Turkey Plasma Focus- The Machine and Scaling Properties S H Saw and S Lee INTI International University, 71800 Nilai, Malaysia Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia e-mail: leesing@optusnet.com.au sorheoh.saw@newinti.edu.my

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

The Plasma Focus 2/2 Axial Phase Radial Phases

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

Comparison (Scaling) Important machine properties: UNU ICTP PFF PF1000 E0 3kJ at 15 kV 600kJ at 30kV I0 170 kA 2MA ‘a’ 1 cm 11.6 cm

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.

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

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

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

Compare Temperatures UNU ICTP PFF PF1000 (from LS lecture) (this estimate) Axial speed 10 12 cm/us Radial speed 25 20 cm/us Temperature 1.5x106 1x106 K Reflected S 3x106 2x106 K After RS comes pinch phase which may increase T a little more in each case Comparative T: about same; several million K

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.

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

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

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

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

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

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

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

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 1/3

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

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)

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 1/2

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

Focus Pinch T, dimensions & lifetime with anode radius ‘a’ Scaling properties-mainly radial phase 2/2 Dimensions and lifetime scales as the anode radius ‘a’. rmin/a (almost constant at 0.14-0.17) 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).

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

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

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.

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

Plasma Focus- The Machine and International School on Magnetohydrodynamics and Fusion Applications (ISMFA 2011) 9-17 September 2011, ITAP, Turunc, Marmaris, Turkey Plasma Focus- The Machine and Scaling Properties S H Saw and S Lee INTI International University, 71800 Nilai, Malaysia Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia e-mail: leesing@optusnet.com.au sorheoh.saw@newinti.edu.my