Current Sheet Axial Dynamics of 2.5 kj KSU- DPF under High Pressure Regime

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1 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT < 1 Current Sheet Axial Dynaics f.5 kj KSU- DPF under High Pressure Regie Agad E. Mhaed, Meber, IEEE, Ali E. Abdu, Meber, IEEE, Mhaed I. Isail, Meber, IEEE, S. Lee, S.H. Saw Abstract In Dense Plasa Fcus (DPF achines, the High pressure regie f peratin can be used as alternative technique t shrt-circuit test as the current sheet tin is inial. The shrt circuit test was perfred t get the right values fr the static paraeters f the achine. High pressure shts f re than 30 bar were perfred n the.5 kj Kansas State University Dense Plasa Fcus KSU-DPF achine t deterine the deviatin f HP values fr shrt circuit values in cputed static inductance and resistance. The test was perfred using varius gases ver a wide range f lecular/atic ass, starting fr hydrgen as the lightest gas up t argn. It was fund that the deviatin in static inductance and resistance cputed fr high pressure ethd is inversely prprtinal t gas lecular ass at a certain pressure. The heavy gases like nen and argn were fund t give the st accurate results. At 60 bar f argn the inductance deviatin was 6.5%, and 14% fr resistance. It was fund als that increasing f gas pressure ver 30 bar using heavy gases like Ar r Ne gives n effective iprveent f the cputed static ipedance. Snwplw del was used t predict the axial psitin and the axial speed f the current sheet during the high pressure regie. The del shwed that the average axial speed in heavy gases like argn was 0.8 c/μs, whereas in hydrgen, it was 1.6 c/μs. Index Ters plasa fcus, high pressure discharge, static inductance, plasa resistance, axial speed, snwplw del T I. INTRODUCTION HE static ipedance f the DPF capacitr bank is cnsidered an iprtant paraeter in deterining the behavir f the current wavefr supplied t the achine. Hence, it affects the neutrn yield and x-ray eissin f such Manuscript received Octber 1, 011. This wrk was funded by the departent f echanical and nuclear engineering, Kansas State University, USA. Agad E. Mhaed, departent f echanical and nuclear engineering, Kansas State University, Manhattan, KS USA (eailengaes@ksu.edu. Ali.E. Abdu, departent f echanical and nuclear engineering, Kansas State University, Manhattan, KS USA (crrespnding authr, phne: ; fax: ; e-ail: aeabdu@ k-state.edu. Mhaed.I. Isail, departent f echanical and nuclear engineering, Kansas State University, Manhattan, KS USA (eailisail1@ksu.edu. S. Lee, INTI Internatinal University, Nilai, Malaysia, Institute fr Plasa Fcus Studies, Melburne, Australia (e-ail: leesing@ptusnet.c.au. S. H. Saw, INTI Internatinal University, Nilai, Malaysia Institute fr Plasa Fcus Studies, Melburne, Australia (e-ail: (srheh.saw@ newinti.edu. achine [1],[].The plasa fcus achines f Mather-type have been recently classified int tw types accrding t the value f their static inductance [3]. The st reliable ethd t deterine the DPF static paraeters C, L, and R is the shrt circuit (SC test. On the ther hand the SC test is technically difficult t perfr specially in high current achines, s it ay be preferred t perfr a high pressure (HP test t get apprxiate values fr the static paraeters [4]. The assuptin is that: at high pressures, the current sheet hardly ves as the high gas density suppresses the current sheet tin; the gas density in the high pressure regie is abut 5 t 30 ties re than the ptiu gas wrk density. The discharge current predinantly ges thrugh diffusive hic regie rather than electragnetic regie. Althugh the high pressure gas greatly slws dwn the tin f the current sheet, a sall displaceent still exists, which adds an aunt f inductance and resistance t the circuit; thus causing an ver-estiatin f the static paraeters [1]. II. THE KSU-DPF EXPERIMENT A. KSU-DPF Specificatins The KSU-DPF is a Mather type geetry cpsed f three ain parts: the capacitr bank cprises an Aervx capacitr f 1.5 μf capacitance with rated vltage 0 kv and stred energy.5 kj. The capacitr is charged using a General Atics GA pwer supply with rated vltage 30 kv and 8 kj/s. The capacitr is cnnected t the electrdes thrugh a thyratrn TDI1-00k/5kV, 10 ns jitter. The central ande is a sei-hllw cpper rd with 100 active length and uter diaeter 15. The ande is surrunded by a squirrel cage cathde ade f 6 equally spaced rds at a distance 9 fr the center f ande. The ande base is insulated fr the cathde using a Pyrex tube f 68 length and 1.6 wall thickness. Bth cathde and ande are unted inside a stainless steel chaber with tw glass windws. The current is easured using a Rgwski cil in the di/dt de, and then nuerically integrated t btain the current wavefr. A Nrthstar high vltage prbe HV5 60/100 kv DC/AC 80 MHz was used t easure the vltage wavefr acrss the tube. B. Rgwski Cil Cnsideratins The discharge current wavefr btained fr the nuerically integrated Rgwski cil signal shws baseline

2 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT < Fig. 1. Rgwski cil integrated signal, with and withut cpensatin. shift as shwn in Fig. 1. Electragnetic pickup, and pwer lines interference are ptential rt causes f the baseline shift [5]; the ffset culd als result fr grunding prbles r nn-syetrical tplgy effects with the unting f the cil s that the cil nt nly nitrs the current passes inside, but als the current passes utside the cil [6]. Three nuerical ethds were intrduced t reslve the prble. The first ethd uses a cbinatin f digital filters n the riginal di/dt cil signal. Origin prgra was used t perfr such prcessing. The secnd ethd is t find the average f the signal envelpe; this technique was perfred by fitting the psitive peaks f the wavefr as well as the negative peaks then calculating the average f bth fitted curves. Afterwards, this average curve was subtracted fr the riginal wavefr. The third ethd was perfred by capturing the first few icrsecnds befre the signal rise, and the final few icrsecnds clse t the end f the daped curve. The tie space in between the tw prtins was interplated, the interplated curve represents the base shift. Hence it was subtracted fr the riginal wavefr t btain the cpensated current withut the baseline shift. The first and last ethd gave better predictin t the baseline shift; Fig. 1 indicates the riginal and the cpensated curves using the first ethd. C. High Pressure Regie The ptiu wrking pressure fr KSU-DPF achine is abut 4bar in deuteriu and bar fr nen. The high pressure regie was perfred under pressure range bar. The capacitr is charged t 17 kv. The wrking gases were argn, nen, heliu, deuteriu, and hydrgen. The current wavefr was easured using Rgwski cil then analyzed using the RLC analysis [1]. The resulting values fr the inductance and resistance incrprate cntributins due t the tin f the current sheet. This tin has a dependence n the pressure and gas lecular weight. By studying the results in the varius gases this extraneus cntributin ay be re readily understd and eliinated. III. EXPERIMENTAL WORK A shrt circuit test was perfred first t find the static paraeters f the achine. A special cnnectr was achined with a diaeter and length equal t the ande base. The cnnectr was used t cnnect the ande and cathde plates, and cpensate the ipedance change due t reval f the real ande and cathde. High pressure tests were perfred t deterine the achine static paraeters; the riginal ande and cathde were returned back during the test. The chaber was filled with varius gases at pressures fr bar with 10 bar increent step. A fast respnse Rgwski cil was fabricated t pick up the current signal. The capacitr was charged every sht t 17 kv, and then the sht was perfred by turning n the thyratrn switch. The current then flwed fr the ande t the cathde thrugh the gas ediu in between. The experient was repeated three ties at each pressure t avid incnsistent shts. IV. THEORETICAL MODEL The snwplw del was used t siulate the tin f the current sheet during the axial phase and t calculate the inductance induced during the current sheet tin [7]. Assuing ne diensinal del, with a planar current sheet perpendicular t the axis f the electrdes. This apprxiatin is nearly true at high pressure [8], [9]. The change f entu equatin due t the frce fr (JxB. dv z d dz ( t f ( b a z ( t dt dt dt b ( f ci r dr ( r a Where a, and b are the radii f the ande and cathde respectively. ρ is the initial gas density f gas, μ is the pereability f the free space. f, and f c are the snwplw ass swept up factr, and current factr respectively. Fig.. The siulated current and the experiental current fr deuteriu at 40 bar. (1

3 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT < 3 Therefre, dz ( t ln( b / a z ( t ( f ci dt dt 4 f ( b a ( Let I nr =I/I, is the nralized current wavefr, integrate t find the displaceent f the current sheet z(t. 1/ nr z(t= U I dt dt Where, U ln( b / a( f I c 4 ( f ( b a is the characteristic axial transient speed fr which the axial speed will be, dz U I dt (5 nr dt z The theretical current was calculated as sinusidal wave dified by a daping functin I ( t I t e sin( t, where α is the expnential daping cefficient ( R /L, and is the natural angular frequency ( ; d is the resnant radian frequency ( 1/ LC. The theretical current was atched t the experiental current wavefr by changing three factrs; the frequency, the daping factr α, and aplitude I, see Fig.. The current wavefr, the d (3 (4 Fig. 4. HP inductance and resistance deviatin versus the lecular ass f the used gas (at 60 bar capacity fr the capacitr, and the charged vltage supplied t the circuit were used t calculate the ipedance f the circuit, these calculatins can be btained fr SC analysis. Hence the axial psitin and axial speed can be calculated as a functin f tie. 4 t e (1 cs( t t e ( cs( t U 3 t z ( t e sin( t ( 4 t ( e t 1/ (6 The axial speed will be, t t 1e e cs( t dz ( t U ( (7 t dt 4 z ( t e sin( t ( Therefre, the tube inductance due t the tin f current sheet can be deterined as a functin f the psitin. b L p ln( Z ( t (8 4 a The del was applied t previus experiental data fr literature [8]-[10]. These wrks assued apprxiate sinusidal current wavefr I ( t I sin( t withut the daping effect. Our daped del illustrated re precise atching t thse experiental data in axial psitin and axial speed calculatins. n Fig. 3. The calculated resistance and inductance fr the RLC del versus pressure. V. RESULTS A. Experiental results The SC test paraeters were picked up fr the KSU-DPF achine, fr capacitr with C =1.5 μf, and V =17 kv, the reversal rati f = , and the peridic tie T= s.

4 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT < 4 Therefre L =15nH, R =14.4 Ω, I =153 ka. Then the Rgwski calibratin factr (I /V 1 = A/V, where V 1 is the first peak f Rgwski integrated signal crrespnding t the current peak I. The current wavefrs fr the HP tests were analyzed using RLC circuit analysis as stated befre. The results shw nticeable difference in inductance and resistance. This difference was drpping as the pressure increased Fig. 3, especially in light gases. The iniu calculated inductance and resistance recrded at 60 bar argn were 133nH, and 17.1 Ω respectively. The axiu values recrded at 30 bar hydrgen were 145nH, and 7.6 Ω. This shws that the tin f current sheet is greater in light gases than in the heavy gases. The difference in between HP and SC results was cnsidered as a deviatin in L and R when using HP ethd as an apprxiatin t find the static paraeters. This deviatin was calculated as a functin f lecular ass f the wrking gas. Fig. 4 indicates the deviatin percentage f resistance and inductance at 60bar; it was fund that the deviatin percentage was inversely prprtinal t the lecular ass. At 60 bar the deviatin in calculated inductance varied fr 14% fr hydrgen t 6.5% fr argn. The resistance deviatin at the sae cnditins varied fr 54% fr hydrgen t 13.7% fr argn. B. Theretical del results Snwplw del was used t plt the axial psitin, speed and acceleratin in the high pressure regie. Fig. 5 shws the axial paraeters utput. The slid lines express results fr the daped sinusidal current del and the dtted lines expresses the nn-daped sinusidal current del. These curves are crrespnding t the first half cycle f the current wavefrs. The del results indicated difference in axial psitin f abut 30% and in speed f 15% between the tw cases f current wavefrs. Table A indicates the tube inductance (which is the SC inductance less the ttal inductance during plasa tin, crrespnding axial psitin, and speed in varius cases. The average axial speed was calculated fr each gas n the range f the wrked pressure. The average speed in the high pressure varies fr 0.79 c/μs in argn t 1.60 c/μs in hydrgen. VI. CONCLUSION At the high pressure regie the KSU-DPF is perating at lw shck wave speed; in such regie the cupling f energy prvided t the plasa is predinantly thrugh diffusive electrical discharge rather than electragnetic pistn-like. Nevertheless the data des indicate that there is dwnstrea tin f the diffusive structure which we interpret as due t electragnetic drive. Mrever the data fr the average 0.5 speed is fund t be prprtinal t (1/ extending t the highest pressures which indicates that the speeds can be cnsidered as electragnetically driven even thugh we knw the diffusive structure is electrically resistive. This interpretatin is in a grss sense valid as evident fr ur analysis which shws in every case a significantly larger Fig. 5. Snwplw del using MathCAD dynaic sheet. Slid lines indicate the daped current del; the dtted lines indicate the sinusidal current del. (data fr nen at 40 bar, 17 kv. inductance and resistance fr the HP tests when cpared with the SC tests. We are therefre presenting this technique as a useful alternative ethd t the shrt circuit test in rder t find ut the static paraeters fr the achine. The induced errr percentage due t the tin f current sheet was calculated using the apprxiate del. These results can be used as a reasnable first rder crrectin t the values calculated with HP tests, and can be applied fairly n ther achines with different geetries and energy scales. Under the high pressure regie, it was fund that the speed f the current sheet is apprxiately ne fifth the ptiu speed in the nral wrking cnditins. The deviatin in L and R is 0.5 prprtinal als t (1/ where ρ is the gas density. TABLE A Average axial psitin and axial speed values at different pressures Gas Pressure (bar tube inductance Lp (nh Z (c V (c/μs Average speed (c/µs Argn Nen Heliu Deuteriu Hydrgen

5 > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT < 5 Finally it shuld be nted that althugh the use f the daped sinusidal current in the snwplw equatin f tin prduces re accurate results than the use f an undaped sinusidal current, but it is still an apprxiatin when cpared t the ethd f using the equatin f tin cupled t the circuit equatin. The cupled-equatins ethd allws fr the tin and the current t be derived as the tw slutins f the tw equatin syste. The nature f the prble is such that the current wavefr is a daped sinusid with nn-linear tie-varying daping factr as well as frequency; these are crrectly incrprated int the pintby-pint slutins as the cupled equatins are nuerically slved [1,11]. Nevertheless the use f a daped sinusidal current in the equatin f tin ay still be used as a sipler alternative fr analytical purpses. REFERENCES [1] S.H. Saw, S. Lee, F. Ry, P.L. Chng, V. Vengadeswaran, A.S.M. Sidik, Y.W. Leng and A. Singh, "In situ deterinatin f the static inductance and resistance f a plasa fcus capacitr bank," Review f Scientific Instruents, vl. 81, n. 5, pp [] W A. Bernard, et al, Scientific Status f Plasa Fcus Research, J. Mscw Phys. vl.8, n., pp [3] S. Lee, S. Saw, A. Abdu and H. Trreblanca, "Characterizing plasa fcus Devices Rle f the static Inductance Instability phase fitted by analus resistances," J.Fusin Energy, vl. 30, n. 4, pp [4] S S. Lee, Experients With the ICTP-UM 3.3 kj Plasa Fusin Facility, Spring Cllege n Plasa Physics, Internatinal Centre fr Theretical Physics, Trieste, Italy, May 7 June [5] D.A. Ward and J.L.T. Exn, "Using Rgwski cils fr transient current easureents," Engineering Science and Educatin Jurnal, vl., n. 3, pp [6] S. Lee, S. Saw, R. Rawat, P. Lee, R. Vera, A. Talebitaher, S. Hassan, A. Abdu, M. Isail, A. Mhaed, H. Trreblanca, S. Al Hawat, M. Akel, P. Chng, F. Ry, A. Singh, D. Wng and K. Devi, "Measureent and prcessing f fast pulsed discharge current in plasa fcus achines," J.Fusin Energy, pp [7] L.R.M. G, "A cent n the shape f the current sheet in a caxial acceleratr," J.Phys.D, vl. 11, n. 13, pp [8] M. Mathuthu, T. G. Zengeni, and A. V. Ghlap, Measureent f agnetic field and velcity prfiles in 3.6 kj United Natins University/ Internatinal Center fr theretical physics plasa fcus, Phys. Plasas, vl. 3, n. 1, pp , [9] S. Al-Hawat, "Axial velcity easureent f current sheath in a plasa fcus device using a agnetic prbe," Plasa Science, IEEE Transactins n, vl. 3, n., pp [10] H. Bhuyan, S. R. Mhanty, N. K. Neg, S. Bujarbarua, and R. K. Rut "Magnetic prbe easureents f current sheet dynaics in a caxial plasa acceleratr," Measureent Science and Technlgy, vl. 14, n. 10, pp /14/i=10/a=305. [11] S Lee. Radiative Dense plasa Fcus Cputatin Package (011: RADPF ;

Current sheet axial dynamics of 2.5 kj KSU-DPF under high pressure regime

Current sheet axial dynamics of 2.5 kj KSU-DPF under high pressure regime This is the author s final, peer-reviewed manuscript as accepted for publication. The publisher-formatted version may be available through the publisher s web site or your institution s library. Current