Modeling D-D Operation of the UW IEC Experiment

Transcription

1 Modeling D-D Operation of the UW IEC Experiment J.F. Santarius, R.P. Ashley, G.L. Kulcinski, B.B. Cipiti, S.Krupakar Murali, G.R. Piefer, R.F. Radel, J.W. Weidner University of Wisconsin US-Japan IEC Workshop, University of Wisconsin, October 9-1, 22

2 Outline Atomic physics and current generation considerations Improvements to speed of code Results of modeling ion and electron currents in the UW IEC device Neutron and proton production predictions and comparison with experiment JFS 22

3 Atomic Physics Cross Sections Were Corrected to Use kev/amu Example: D + D Charge Exchange as Implemented in Mathematica Notebook 1.µ µ1-19 à H + charge-exchange with H (G) s á Chebyshev fit In[3]:= lscxxshp1htohhp1cheb = Import@dataDir<> "cx_xs_h+htohh+_cheb.dat"d@@83, 4<DD êê Flatten Out[3]= , , , ,.8789, , , , ,.12, 63.< In[31]:= CxXsHp1HtoHHp1Cheb@amu_, EkeV_D = 1 4 Cheb@lsCxXsHp1HtoHHp1Cheb, EkeVêamuD; s Hm 2 L 1.µ µ1-2 1.µ1-2 5.µ1-21 Data comes from the IAEA AMDIS database. 1.µ Ion energy HkeVêamuL JFS 22

4 Many Atomic Physics Reactions Have Been Implemented Fitting functions and data input directory Neutral-neutral and ion-neutral elastic collisions Charge exchange à H + charge-exchange with H (G) à H + charge-exchange with H 2 (G) à H + charge-exchange with He (G) à H + charge-exchange with He + (G) à He + charge-exchange with H (G) à He + charge-exchange with He (G) à He + charge-exchange with He + (G) à Combined H + charge-exchange plots à Combined H + and He + charge-exchange plots Dissociation à H ionization and dissociation of H 2 (G) à H + ionization and dissociation of H 2 (G) à He + ionization and dissociation of H 2 (G) à e - ionization and dissociation of H 2 (G) Ionization à H ionization of H 2 (G) à H + ionization of H (G) à H + ionization of H 2 (G) à H + ionization of He (G) à H + ionization of He + (G) à Combined H + ionization plots à He + ionization of H (G) à He(2s1) Penning ionization of H (G) à He + ionization of He (G) à He + ionization of He + (G) à He +2 ionization of He (G) à He +2 double ionization of He (G) à Combined He + and He ++ ionization plots à e - ionization of H (G) à e - ionization of H 2 à e - ionization of He à e - ionization of He + à Combined monoenergetic e - ionization cross-section plots à Combined Maxwellian e - ionization reaction rate plots Secondary electron emission JFS 22 Sputtering

5 UW Experiment Key Modeling Input Parameters Fuel Neutral gas pressure Neutral gas density Anode radius Cathode radius potential difference D only.27 Pa (2 mtorr) 6.4 x 1 19 m m.5 m 8 kv JFS 22

6 Atomic Physics Effects Dominate the Present Operating Regime yhml Secondary electron emission and sputtering important JFS r c Ion-impact ionization r l Charge exchange dominates r l = lower radius for tracking Multiple ion passes r b Electron-impact ionization produces source plasma r b = ion birth radius r u = upper radius for tracking Cathode xhml r u r a Anode Child- Langmuir potential contours shown in red.1-1 Pa (~1-1 mtorr) moderately collisional plasma Conditions for ion tracking V a -V(r u ) = 1 kv V(r l ) - V c = 1 kv

7 Child-Langmuir Electrostatic Potential Profile Is Calculated and Used to Generate Radial Velocity Profile Child-Langmuir radial potential profile P otential H k V L location location Resulting radial velocity profile JFS 22 Ion radia lv elocit yhmêsl Radius HmL 4µ1 6 3µ1 6 2µ1 6 1µ1 6 location Radius HmL He ++ D + He + location

8 Charge Exchange Attenuates Initial Ion Current as Ions Oscillate Radially Fraction of origina lcurren t Region where charge exchange creates a 2 nd generation, low-energy ion grid Pass 1 Pass 3 Pass 2 Region of low ion energy, where charge exchange has little effect on the ion distribution and current is kept constant. Pass rhml JFS 22

9 Similar, but Not the Same, Behavior Occurs for Ions Born at Radii Smaller than the Anode Radius Fraction of origina lcurren t Evolution of ions that start at r a /3 or 2r a / rhml JFS 22 Ions startat 1 ra ê 3 Fraction of origina lcurren t Ions start at 2 ra ê rhml

10 Ion-Current at Radial Position r Can Be Calculated for Arbitrary Birth Position r b Fitting these functions (using Mathematica s ListInterpolate function) sped up key calculations by >5 times. Ions starting at r = r b Ions starting at r = Inward Attenuated Current Outward Attenuated Current J in r(m) shml rhml r b (m) J out r(m) shml.2 r r HmL.1 b (m) JFS 22

11 Charge-Exchange and Ionization Events Create New-Generation Deuterons and Electrons Creation rates for first two generations of deuterons and electrons S ource Hm -1 s -1 L rhml JFS 22 Electron Electron Production Production Rate Rate 1 st generation New-Generation 2 nd generation S ource Hm -1 s -1 L rhml New-Generation Deuteron Deuteron Production Production Rate Rate 1 st generation 2 nd generation

12 Two-Generation Calculation of Proton Production Falls Short of Experimental Value Experimental D-D proton production at 8 kv and 3 ma is 2x1 7 protons/s Two-generations of the present computational method give ~1 6 protons/s total Main contribution stems from charge-exchange neutrals and radially moving ions reacting with background gas. Converged-core and counter-streaming-ion fusion terms give very small contributions. Following several generations of ions may pick up the factor of ~2 required to agree with experiment. Neglected effects, such as fusion of embedded ions, may also contribute. JFS 22

13 Summary Fitting current attenuation functions instead of calculating integrals as needed sped up code by >5 times. Fusion product production as a function of radius has been estimated. Using only the initial current plus first and second generations of created ions gives values ~2 times lower than those found in the UW IEC experiments. Preliminary indications are that following several more generations of ion production may reconcile these differences. JFS 22