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Ion Beams and Plasma Streams- some results from numerical experiments-

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### Ion Beams and Plasma Streams- some results from numerical experiments-

### Scope of discussion

### Sequence of shadowgraphs of PF Pinch- M ShahidRafique PhD Thesis NTU/NIE Singapore 2000

### Much later…Sequence of shadowgraphics of post-pinch copper jetS Lee et al J Fiz Mal 6, 33 (1985)

### Comparing large and small PF’s- Dimensions and lifetimes- putting shadowgraphs side-by-side, same scale

### Flux out of Plasma Focus

### Modelling the flux-reporting preliminary work

### From the above; estimate ions/m2 per shot

### Number of Ions in beam

### We intend to refine these computation

### Latest development

### Ion beam post-pinch plasma stream calculations Some preliminary Results- INTI IU-IAEA collaboration

### Concluding Summary

S Lee & S H Saw

INTI International University, 71800 Nilai, Malaysia Institute for Plasma Focus Studies, Chadstone VIC 3148 Australia

e-email: [email protected]; [email protected]

Use of the Lee Model code to study scaling of deuteron beams for consideration of damage and materials, nano-materials modification and synthesis.

Related scaling of Fast Plasma Stream and anode sputtered material

Highest post-pinch axial shock waves speed ~50cm/us M500

Highest pre-pinch radial speed>25cm/us M250

Slow Copper plasma jet 2cm/us M20

Anode radius 1 cm 11.6 cm

Pinch Radius: 1mm 12mm

Pinch length: 8mm 90mm

Lifetime ~10ns order of ~100 ns

Charged particle beams

Neutron emission when operating with D

Radiation including Bremsstrahlung, line radiation, SXR and HXR

Plasma stream

Anode sputtered material

Ion beam flux

Preliminary work shows the quantity ion beam flux (Fib ions per m2 per sec) x pulse length (t sec) which has the units of number of ions per m2 (per shot) is:

Fibt = Cn Ipinch2zp[ln(b/rp)]/ (prp2 U1/2)

All SI units: calibration constant Cn =8.5x108 ; model was calibrated against an experimental point at 0.5MA

Ipinch=pinch current

zp=pinch length

b=outer electrode, cathode

rp=pinch radius

U=beam energy in eV where in this model U=3x (dynamic induced voltage)

Numerical Expt for PF1000 based on following fitted parameters:L0=33 nH, C0=1332 uF, b=16 cm, a= 11.6 cm, z0=60 cm r0=6.3 mWfm=0.14, fc=0.7, fmr=0.35, fcr=0.7V0=27 kV, P0= 3.5 Torr MW=4, A=1, At=2 for deuterium

Results are extracted from dataline after shot:

Yn=1.16x1011 neutrons, ni=3.87x1023 per m2,

Ipinch=8.63x105 A, zp=0.188 m, b/rp=16 cm/2.23 cm, ln(b/rp)=1.97,

U=3Vmax=3x4.21x104 =1.263x105 V; fusion x-section σ

=0.0238barns = 2.38x10-30 m2.

Numerical Expt for INTI PF based on following fitted parameters:L0=110 nH, C0=30 uF, b=3.2 cm, a= 0.95 cm, z0=16 cm r0=12 mWfm=0.073, fc=0.7, fmr=0.16, fcr=0.7V0=15 kV, P0= 3Torr MW=4, A=1, At=2 for deuterium

Results are extracted from dataline after shot:

Yn=1.14x107 neutrons, ni=3.5x1023 per m2,

Ipinch=1.22x105 A, zp=0.014 m, b/rp=3.2cm/0.12 cm, ln(b/rp)=3.28;

U=3Vmax=3x2.52x104 =0.756x105 V; fusion x-section σ =0.0112barns=1.12x10-30 m2.

For PF1000 (at 500 kJ) we obtained

Jbt =4.3x1020 ions/m2 per shot=4.3x1016 ions/cm2 per shot at 126 keV

(~1kJ/cm2; 109 W/cm2 if pulse of 1 ms)

For INTI PF (at 3 kJ) we obtained

Jbt =4.7x1020 ions/m2 per shot

=4.7x1016 ions/cm2 per shot at 76 keV

Quantity Jbt is the same for small and big PF

Taking pinch radius as effective area for beam

For PF1000 rp=2.23 cm (model computation)

Thus number of ions per pulse=6.7x1017 at effective energy of 126 keV(14kJ 3% E0)

For INTI PF rp=0.12 cm (model computation)

Thus number of ions per pulse=2.1x1015 at effective energy of 76 keV

Number of ions per pulse is 300 x higher for PF1000 compared to INTI PF(26J 1% E0)

We have the neutron yield for each of the devices- numerical expts have been compared to actual measurements and found to agree-typically 1011 per shot for PF1000

We will compute plasma stream energy by looking at the quantity EINP (work done by magnetic piston as % of stored energy) –typically 13% E0 (65kJ) for PF1000; and 9% E0 (270 J) for INTI PF

These will be carried out in the next period.

Modelling

Ion beam fluence

Post focus axial shock waves

Plasma streams

Anode sputtered material

The ion fluence , 2-6x1020 ions/m2

average ion energy 40-250 keV and

beam damage factor 2x1010 Wm-2s0.5

are found to be independent of storage energy being relatively constant over the range of devices, from kJ to MJ.

The beam size (on exit) and duration increase with storage energy, primarily as a function of anode radius.

The beam energy increases with storage energy 1-3% ; as does the fast plasma stream energy exiting the pinch 5-10% .

Anode sputtered materials, slow jet typically 1-3%.

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