Siam Physics Congress SPC 2013 Thai Physics Society

Siam Physics Congress SPC 2013 Thai Physics Society on the Road to ASEAN Community 21 -23 March 2013 Numerical Experiments on Ion Beams from Plasma Focus S H Saw 1, 2 & S Lee 1, 2, 3 1 INTI International University, 71800 Nilai, Malaysia 2 Institute for Plasma Focus Studies, Chadstone, VIC 3148, Australia 3 University of Malaya, Kuala Lumpur, Malaysia e-mail: sorheoh. saw@newinti. edu. my; leesing@optusnet. com. au

Summary- Previous work • Much work using variety of diagnostics reported on plasma focus ion beams, mainly experimental • Confusing picture- even units are confusing un-correlated across devices and experiments • No benchmark or scaling patterns appears to have been reported until: • Our Previous work: We adapted beam- gas target neutron yield mechanism for D beams from plasma focus • Our Previous results: (first plasma focus results on ion beam scaling- D) Ø Ion number fluence: 2. 4 -5. 7 x 1020 ions m-2; independent of E 0 Ø Ion Number: 1. 2 -2 x 1015 ions per k. J; dependent on E 0 School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Summary- New work Our New work: First principle derivation of ion number flux and fluence equations applicable to all gases. New results: Ø Fluence, flux, ion number and ion current decrease from the lightest to the heaviest gas Ø Energy fluence, energy flux and damage factors are constant from H 2 to Ne; but increase for the 3 high-Z gases Ar, Kr and Xe due to to radiative collapse. Ø The FIB energy has a range of 4 -9% E 0. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief review of existing work • Measurements of ion beams from PF’s have produced a wide variety of results using different units; • Less correlated than expected • No discernable pattern or benchmarks. • In summarizing experimental results, Bernard el al 1 in 1996, it was reported that total yields of ions reach 1010 -1014 sr-1 depending on energetics and experimental conditions. • In a single discharge fast ions are emitted from point-like (submm) sources mostly as narrow micro-beams with duration times of 2 -8 ns forming intense bunches having total powers reaching 1011 to 1012 W. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief Review: Takao et al 2 2003 • 19. 4 k. J (43 m. F, 30 k. V 500 k. A peak current) PF published nitrogen ion beam power brightness of 0. 23 GW cm-2 sr (maximum ion energy at 0. 5 Me. V) using a solid anode; • and 1. 6 GW cm-2 sr (maximum ion energy of 1 Me. V) using a hollow anode. • Peak ion current densities of 1100 -1300 A cm-2 (50 -60 ns) were recorded. [which would give a beam ion current <1 k. A!!] School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief Review- Bhuyan et al 3, 2011 • reported beam ion densities of 9. 7 -15. 5 x 1019 m-3 (ion energy 15 -50 ke. V) at the aperture of Faraday Cups for 0 -25 degree angular positions 6 cm from the anode top in a 40 k. V 2. 2 k. J neon PF. • Track densities (CR-39 film) had a maximum value of 10. 9 x 109 tracks m-2 at 30 degrees. • In another experiment, Bhuyan 6 operating a 1. 8 k. J methane PF quoted a flux of 2 x 1022 m-2 s-1 multiple-charged carbon ions (50 -120 ke. V). School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief Review- Kelly et al 4 • UBA PF II (4. 75 k. J 30 k. V) in nitrogen; used Faraday Cup and Thomson spectra to measure nitrogen ions (50 -1000 ke. V) recording 3. 2 x 1013 ions/sterad with energy content of 0. 74 J/sterad. • In another experiment 5 same machine in dueterium, Kelly surmised a total number of 1015 deuterons at 20 -50 ke. V. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief Review- Szydlowski et al 7 • foil-covered CR-39 track detectors states that the PF-1000 generates 105 ions/mm 2 (energy above several dozen ke. V) with neutron yields of 1010 -1011 neutrons/shot. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief review- Bostick et al 8 • 5. 4 k. J PF using TOF and ion filters recorded fluence of 1014 (Me. V. sr)-1 for the energy spectrum of deuterons (0. 3 -0. 5 Me. V) with FWHM of 40 -60 ns and 1012 (Me. V. sr)-1 (at 1 -9 Me. V) with FWHM of 10 -20 ns. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Brief Review- Summary • • Many different experiments Many different machines Different gases Many types of diagnostics Many sets of data Data- some total (FC), some sampling (track detectors) ie not all ions recorded Different perspectives, different units: number sr-1; bunch power in W; beam power brightness in GW cm-2 sr ; ion current densities in A cm-2 ; beam ion densities in m-3 ; tracks m-2 ; ions/sterad ; J/sterad ; total ion numbers; flux in m-2 s-1 ; ion fluence in (Me. V. sr)-1 • Correlation among experiments? Benchmarking? Scaling? Obvious errors of orders of magnitude!! School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Our numerical experiments on Ion Beams • The ion beam numerical experiments adds on as a branch to the integrated view which our numerical experiments strive to present of the plasma focus School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Philosophy, modelling, results & applications of the Lee Model code Philosophy School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Latest development Modelling: Ion beam fluence Post focus axial shock waves Plasma streams Anode sputtered material School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy Latest

Summary of basic physical picture School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Plasma Focus Pinch with plasma stream (Paul Lee- INTI PF) School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Emissions from the PF Pinch region Mach 500 Plasma stream Mach 20 anode material jet School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Sequence of shadowgraphs of PF Pinch- (M Shahid Rafique Ph. D Thesis NTU/NIE Singapore 2000) School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, Highest post-pinch axial shock waves speed ~50 cm/us M 500 their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Extracted from V A Gribkov presentation: IAEA Dec 2012 V N Pimenov 2008 Nukleonika 53: 111 -121 School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Comparing large and small PF’s- Dimensions and lifetimes - putting shadowgraphs side-by-side, same scale Anode radius 1 cm 11. 6 cm Pinch Radius: 1 mm 12 mm Pinch length: 8 mm 90 mm Lifetime ~10 ns order of ~100 ns School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Flux out of Plasma Focus – Charged particle beams – Neutron emission when operating with D – Radiation including Bremsstrahlung, line radiation, SXR and HXR – Plasma stream – Anode sputtered material School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Basic Definition of Ion Beam characteristics • Beam number fluence Fib • Beam energy fluence (ions m-2) (J m-2) Flux =fluence x pulse duration • Beam number flux Fibt • Beam energy flux School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy (ions m-2 s-1) (W m-2)

Our starting point: the mechanism described by V. A. Gribkov et al in J Phys. D 40, 3592 (2007) • Beam of fast deuteron ions produced by diode action in thin layer close to the anode; plasma disruptions generating the high voltages. Beam interacts with the hot dense plasma of focus pinch column to produce the fusion neutrons. • In our modeling of the neutron yields, each factor contributing to the yield is estimated as a proportional quantity. The yield is obtained as an expression with proportionality constant. The neutorn yield is then calibrated against a known experimental point. • We start with the neutron yield (rather than the ion beam number) because our method requires a calibration point; and for neutron yields by placing published yields on a chart we can obtain a good fitted calibration point. Had we started with the D ion beam number, we would not have been able to get a reliable calibration point School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Ion beam flux and fluence equations Ion beam flux Jb =nbvb where nb= number of beam ions Nb divided by volume of plasma traversed vb = effective speed of the beam ions. All quantities in SI units, except where otherwise stated. Note that nbvb has units of ions per m-2 s-1. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

We derive nb from pinch inductive energy considerations. Total number of beam ions Nb (each ion mass Mmp, speed vb) has KE= (1/2) Nb Mmpvb 2 where mp =1. 673 x 10 -27 kg is proton mass; M=mass number of ion e. g. neon ion has mass number M=20. Assume this KE is imparted by a fraction fe of the inductive pinch energy (1/2) Lp Ipinch 2 where Lp =(m/2 p) (ln[b/rp])zp; where m=4 p x 10 -7 Hm-1, b=outer electrode of PF carrying the return current, rp= pinch radius and zp= length of the pinch. The pinch current Ipinch is the value taken at start of pinch. Thus: (1/2) Nb Mmp vb 2 = (1/2) fe (m/2 p) (ln[b/rp]) zp Ipinch 2 ; nb= Nb/(prp 2 zp) nb = (m/[2 p 2 mp]) (fe /M) {(ln[b/rp])/(rp 2)} (Ipinch 2 / vb 2) School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy – (1)

We derive vb from the accelerating voltage taken as the diode voltage U Each ion mass Mmp, speed vb , effective charge Zeff is given KE (1/2) Mmpvb 2 by diode voltage U. Therefore: (1/2) Mmpvb 2 = Zeff e. U where e is the electronic (or unit) charge 1. 6 x 10 -19 C; Hence vb= (2 e/mp)1/2 (Zeff /M)1/2 U 1/2 – (2) School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

From (1) multiplying both sides of equation by vb, we have Algebraic manipulations: nb vb = (m/[2 p 2 mp]) (fe /M) {(ln[b/rp])/(rp 2)} (Ipinch 2 / vb) Eliminate vb on RHS of this equation by using Eqn (2) gives Jb =nb vb = (m/[2 p 2 mp])(fe /M){(ln[b/rp])/(rp 2)}(Ipinch 2)(mp/2 e)1/2(M/Zeff)1/2/U 1/2 = (m/[2. 83 p 2 (emp)1/2])(fe/[M Zeff]1/2){(ln[b/rp])/(rp 2)}(Ipinch 2)/U 1/2 Noting that: (m/[2. 83 p 2 (emp)1/2]) = 2. 74 x 1015. We have: Result: Flux = Jb = 2. 75 x 1015 (fe/[M Zeff]1/2){(ln[b/rp])/(rp 2)}(Ipinch 2)/U 1/2 ions m-2 s-1 School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy (3)

The fluence is the flux multiplied by pulse duration t; Thus: Fluence: Jbt = 2. 75 x 1015 t (fe/[M Zeff]1/2){(ln[b/rp])/(rp 2)}(Ipinch 2)/U 1/2 ions m-2 (4) School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Value of fe The parameter fe is the fraction of energy converted into beam energy from the inductive energy of the pinch. By analyzing neutron yield data 1, 3, 4 and pinch dimensional and temporal relationships 15 we estimate a value of fe =0. 14. This condition fe =0. 14 is equivalent to ion beam energy of 3%-6% E 0 in the case when the pinch inductive energy holds 20% -40% of E 0. Our extensive study of high performance low inductance plasma focus classified 16 as Type 1 shows that this estimate of fe is consistent with data. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

We summarise the assumptions: 1. Ion beam flux Jb is nbvb with units of ions m-2 s-1. 2. Ion beam is produced by diode mechanism (ref). 3. The beam is produced uniformly across the whole crosssection of the pinch 4. The beam speed is characterized by an average value vb. 5. The beam energy is a fraction fe of the pinch inductive energy, taken as 0. 14 in the first instance; to be adjusted as numerical experiments indicate. 6. The beam ion energy is derived from the diode voltage U 7. The diode voltage U is proportional to the maximum induced voltage Vmax; with U=3 Vmax (ref) taken from data fitting in extensive earlier numerical experiments. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Procedure The value of the ion flux is deduced in each situation (specific machine using specific gas) by computing the values of Zeff, rp, Ipinch and U by configuring the Lee Model code with the parameters of the specific machine and specific gas. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Example: Numerical Experiment for NX 2 based on following fitted parameters: L 0=20 n. H, C 0=28 u. F, r 0=2. 3 m. W b=4. 1 cm, a= 1. 9 cm, z 0=5 cm fm=0. 08, fc=0. 7, fmr=0. 2, fcr=0. 7 V 0=14 k. V, P 0= within appropriate P range for each gas School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Range of Pressures PF axial run-down time covers a range which encompasses at least from 0. 5 to to 1. 3 of the short-circuit rise time 1. 57*(L 0/C 0)0. 5. The matched condition with the strongest energy transfer into the plasma focus pinch is well covered within the range; also the range covers conditions of high enough pressures that the focus pinch is almost not ocurring as defined by the condition that the reflected shock is barely able to reach the rapidly decelerating magnetic piston. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Collection of data For each shot the dynamics is computed and displayed by the code; which also calculates and displays the ion beam properties. For H 2, D 2, He, N 2 and Ne the procedure is relatively simple even though Ne already exhibits enhanced compression due to radiative cooling. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

RESULTS Fig 2(a) shows a typical PF discharge current computed for NX 2 and fitted to the measured discharge current in order to obtain the model parameters fm, fc, fmr and fcr 32, 33, 41. Fig 2(b) shows the computed radial trajectories of the radially inward shock wave, the reflected radially outward shock wave, the piston trajectory and the pinch length elongation trajectory. Range of pressures: widest for lightest gas H 2 (1 Torr -70 Torr ). For D 2 and He 1 - 40 Torr; for Ne we successfully ran numerical experiments 0. 110 Torr; N 2 from 0. 1 -6 Torr; Xe 0. 05 - to 1. 8 Torr. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Fig 3 illustrates the different compression of the PF pinch. In H 2, D 2 & He radius ratio ~0. 15 up to 10 Torr then rises towards 0. 2. For N 2 the radius ratio drops from 0. 15 to about 0. 13 over range of operation. Ne shows signs of enhanced compressions 3 - 5 Torr; smaller radius ratio to 0. 08 at 4 Torr. Ar shows strong radiative collapse with radius ratio of 0. 04 (cut-off value) around 2. 0 Torr. Kr strong radiative collapse from 0. 5 -2 Torr; Xe from 0. 3 to 1. 5 Torr. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Fig. 4 a shows the flux in ions m-2 s-1. H 2 : 6 x 1027 at 1 Torr , rises to a peak 1. 9 x 1028 at 25 Torr; pressure of best energy transfer for NX 2 in H 2. The D 2 and He curve show same trend but lower peak flux values at 15 Torr. N 2 shows same trend peaking at 3. 6 x 1027 at 3 Torr. Ne shows an accentuated peak of 6. 6 x 1027 at 4 Torr due to radiative enhanced compression. Ar flux is even more accentuated with 8 x 1027 at 2 Torr. For Kr although the radiative collapse is more severe than Ar, flux is flat at 1. 4 x 1027 at 1 Torr. ; this is due to the much greater energy per ion. Xe shows the same flat flux curve as Kr with a flat central value around 6 x 10 26. Conclusion: Beam ion flux drops as the mass number increases, with accentuating factors provided by radiatively enhanced compression. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Fig 5 a shows the fluence in ions m-2. The shape of the curves and the trend with gases are very similar to the flux The peak values of the fluence (ions m-2) range from 8 x 1020 for H 2 decreasing to 6 x 1018 for Xe; with clearly radiation enhanced values of 2 x 1020 and 1. 7 x 1020 for Ar and Ne respectively. . School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Figure 6 a-c show that the beam ion number per k. J range from 1016 for the lightest gases decreasing to 1. 5 x 1012 for Xe in the radiative enhanced regime. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Although the beam ion number is the lowest (see Fig 6) for the heaviest gases Ar Kr and Xe, yet these beams also carry the largest amounts of energy at 8 -9% E 0 compared to around 5 -8% for the other gases. This is because the energy per ion more than compensate for the low numbers. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

The damage factor defined as power flow density multiplied by (pulse duration)0. 5. This quantity is considered to be important for assessing the utility of a beam for damage simulation of plasma-facing wall materials in fusion test reactors. The results show that the heaviest ions produce the biggest damage factors. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

IV Conclusion In this paper we deduce the flux equation of ion beams in plasma focus for any gas using experimental data from the case of deuterons to obtain a calibration constant for energy fraction. We configure the Lee Model code as the NX 2 using best estimated average model mass and current factors obtained from fitting the computed current traces of several gases with experimentally measured current traces. The flux equation is incorporated into the code and the number and energy flux and fluence from different gases are computed together with other relevant properties. The results portray the properties of the ion beam at the pinch exit. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Results: The ion fluence range from 7 x 1020 for the lightest gas H 2 decreasing through the heavier gases until a value of 1. 7 x 1020 for Ar and decreases further dramatically to 0. 03 x 1020 for Xe. The very small fluence value of Xe is due to the very large energy of the Xe ion, estimated to have average charge state Zeff of 28 and accelerated by exceedingly large electric fields induced in the radiative collapse School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy

Ion Beam Benchmarks: Mather PF Latest • ion number fluence ions m-2 • The number of beam ions: beam ions per k. J for PF’s with typical static inductances L 0 of 33 -55 n. H. • Total beam energy: for NX 2 • Beam current: of Ipeak. • Beam energy fluence: J m-2 • Beam Energy Flux: W m-2 The independence from E 0 of the ion beam fluence is likely related to the constancy of energy density (energy per unit mass) that is one of the key scaling parameters of the PF throughout its E 0 range of sub k. J to MJ 14, 28. School and Training Course on Dense Magnetized Plasma as a Source of Ionizing Radiations, their Diagnostics and Applications 8 -12 October 2012, ICTP, Trieste, Italy