DE-R Four Module + PRS Load Simulation
!
! Rick Spielman 2017-12-07
!
Time-step 4.0e-12
Resolution-time 100e-12
End-time 1.0e-6
Number-prints 5
Execute-cycles all
Grids no
Echo-setup no
Max-points 5001
!
!Start circuit definition
!
! DE-R_rev5b.txt is based on DE-R_rev5a.txt. In this run deck we are splitting the two halves
! of the water lines AND Marxes in half so that we can drive each side of the vacuum disk feed 
! separately. This allows more accurate treatment of the MITLs and the convolute. MITL and Z_flow
! models will be incorporated into the deck. We will divide C by 2X and multiply L and R by 2X.
! Remember that the IOUT/IIN calls are backward in the second branch. We have included the non
! perturbing MZFlow block that calculates Ic, If, Zfl.
!
! DE-R Rev5a.txt is based on DE-R Rev4a.txt. We are including a PRS load using the general 
!  parameters of the Z51 deck used in Z15_rev2_Z51.txt. The exact inductance numbers have
!  been tweaked a bit to be self consistent. We output V, I before the MITL TR and V,I after the MITL.
!
! DE-R Rev4a is based on DE-R Rev4. I am removing all of the extra branches to speed iteration. 
! This forces me to divide all marx and water line impedances and inductances by four
! and to increase the Marx C by 4.
!
! DE-R Rev 3a is based on DE-R Rev 2a. We are lowering the WL impedance to 0.4  (1.6/4) and
! explicitly putting in the water flare impedance of the stack. In addition, the insulator, vacuum flare, 
! and MITL impedances will be rechecked. Goal - explicit identification of all impedance and 
! inductance components.
!
! DE-R Rev 2a uses the DE-R Rev 2 deck with 4 parallel modules that are driving an insulator stack,
! MITL, and e-beam load. We will use 4, separate modules joined to the insulator stack with
! End Branches. This way we can keep the Rev1b structure exactly. We also allow jitter in the 
! Future. Note: the module end branches are in reverse order away from the branch.
!
! DE-R Rev 1 uses the DE Rev 4 as the baseline. We will be changing all the line impedances to
! 2  and will be changing the line lengths. The goal here is to have a driver that delivers a clean 100-ns FWHM pulse to a constant impedance load.
!
! Rev 4 changes the CPL water switch gap to the actual gap 3.75
! also changes the output line to constant 1.3  impedance with a matched load.
!
! Rev 3 Marx switch losses and more accurate water line parameters
! Change marx to 30 stages of 300 nF/stage
!
! Gas switch dimensions from drawings
!
! We start with a total Marx capacitance of 100 nF (exceeds the CPL capacitance). This implies
!   that there will a ringing gain on the CPL. This allows a faster rise time than otherwise to 
!   get to the desired CPL voltage.
!
! CPL capacitance used is 60 nF. This is distributed in a TL that is 85 ns long and
!   has a constant impedance of 1.4 . (C = t/Z = 85/1.4 nF = 60.71 nF)
!
! The sub Marx capacitance is 10 nF at a charge voltage of 100 kV.
! We have a 10-nF sub Marx with 30 cap pairs in series and 15 switches. Vch = 3 MV
! We have 10 sub Marxes in parallel.
! the total Marx capacitance is 100 nF.
! Include 130 m individual cap ESR or 65 m per pair of caps in parallel
!   X 30 stages = 1.95  per sub-Marx
! Assume that there will be 200 nH every two stages. L = 167 nH * 15 = 2.5 H.
!   The total Marx inductance (caps and switches) would be 2.5 H/10 = 250 nH
!
! The matched impedance of a single Marx = sqrt(L/C) = 17.3 .
!   The total Marx impedance is 17.3 /10 = 1.73 
!   Note CPL impedance is 2 .
!   The ESR amounts to ~ 11.3% of the matched impedance.
!
! The switch model will have 15x the length of one switch per sub Marx and then will
! have 10 arc channels (sub Marxes) in parallel.
! 
! We will use a TOTAL inductance of 380 nH for the Marx and L1. This inductance is needed to 
! get the required rise time of the voltage on the CPL.
!
! 
! Main Branch - Branch #1
!
BRANCH
!
! B LEVEL
!
! Marx capacitance and charge voltage
! X4 for four modules
!
RCGround 1e+12 200e-9
Initial VC1 3.0e6

UFO VC1
$V_marx_B
UFO EC1
$E_marx_B

!
! Cap inductance, case & parasitic inductance, and ESR
! ESR = 0.195 for the total Marx (1.95  sub Marx/10)
! Divide R and L by 2 for the 2 modules
!

RLSeries 0.098 12.5e-8

!
! Switch resistance - Martin Model and switch inductance - the total gap for a single
!   switch from DWGs is 0.53 (1.346 cm) gap and 93 psig air X15 = 20.19 cm
!
! Initial switch resistance was chosen to be higher than that printed in the first
! few time steps so as to appear monotonically decreasing in R plots
! A careful few runs showed that 10 G looked best. In any event by 1 ns all of the 
! resistance values are the same.
! 10 switches for 10 sub-Marxes, 2 channels for 2 modules
!  Divide inductance by 2 for 2 modules
!

RLSeries 10e9 25e-9
Var R2 Switch
!dielectric switchtime gap        pressure     nswitch  nchannels
AIR           0.0               0.2019  7.3                10           2
UFO IR2
$I_marx_B
UFO R2
$R_switch_B
UFO ER2
$E_switch_B
UFO QR2
$Q_switch_B

!
! Output Marx header inductance
!

RLSeries 0.00 50e-9

!
! Line 1 (CPL), 60 ns, 1.4 , 42.85 nF
! Divide by 2 for 2 modules
!

TRLine EXP 2.29e-09  2   .7
TRLine LIN 56.0e-09   .7 .7
TRLine EXP 2.29e-09 .7  2

UFO VOUT
$V_CPL_out_B
UFO IOUT
$I_CPL_out_B
UFO EOUT
$E_CPL_out_B
UFO POUT
$P_CPL_out_B
UFO EOUT
$E_CPL_out_B

!
! CPL water switches
! 5 output switches, 4 gap + switch inductance
!  Increase number of channels for the four modules
!

RLSeries 10e9 5e-9
Var R2 Switch
!dielectric switchtime gap         pressure   nswitch  nchannels
H2O          310e-09     0.1016   1.0              5             2

UFO IR2
$I_CPL_sw_B
UFO R2
$R_CPL_sw_B
UFO ER2
$E_CPL_sw_B
UFO QR2
$Q_CPL_sw_B

!
! Line 2, 72 ns, 1.4  constant impedance
!

TRLine EXP 2.29e-09 2 .7

UFO VIN
$V_PFL_in_B
UFO IIN
$I_PFL_in_B

TRLine LIN 68e-09 .7 .7
TRLine EXP 2.29e-09 .7 2

UFO VOUT
$V_PFL_out_B
UFO IOUT
$I_PFL_out_B
UFO POUT
$P_PFL_out_B
UFO EOUT
$E_PFL_out_B

!
! Line 2 water switches
! 7 output switches, 0.5 gap + switch inductance
!  Increase number of channels to four for four modules
!

RLSeries 10e9 5e-9
Var R2 Switch
!dielectric switchtime gap      pressure     nswitch  nchannels
H2O         400e-09    0.0127   1.0                    7               2

UFO IR2
$I_PFL_sw_B
UFO R2
$R_PFL_sw_B
UFO ER2
$E_PFL_sw_B
UFO QR2
$Q_PFL_sw_B

!
! Output Line (OL),  72 ns, 1.4  constant impedance
!  Divide by four for four modules
!

TRLine EXP 2.29e-09 2 .7

UFO VIN
$V_OL_in_B
UFO IIN
$I_OL_in_B

TRLine LIN 70e-09 .7 .7

UFO VOUT
$V_OL_out_B
UFO IOUT
$I_OL_out_B
UFO POUT
$P_OL_out_B
UFO EOUT
$E_OL_out_B

!
!  ********* Water flare transition external to the insulator stack ****************
!  Router = 1.165 m , stack outer = 1.1 m, constant 13.35-cm gap, l = 1.96 ns
!  Zouter = 0.76 , Zinner = 0.81   Divide by 2X
!

TRLine LIN 1.96e-9 0.76 0.81

!
!   ***********************  Insulator stack  *****************************
! The water/vacuum interface Router=1.1 m, Rinner=1.0 m, height=13.35 cm (0.64-cm grading rings) 
!  Plastic height is 11.43 cm. L per side = 2.1788 nH
!

RLSeries  0.0    2.1788E-9

!
UFO VOUT
$V_stack_B
UFO IOUT
$I_stack_B
UFO POUT
$P_stack_B
UFO EOUT
$E_stack_B

!
!   **************************  First vacuum piece inside insulator  *****************************
!  Constant 13.35 cm height, Router = 1 m, Rinner = 0.975 m
! Inductance = 0.676 nH
!

RLSeries  0.0    0.676E-9

!
!
!   **************************  Vacuum flares  *****************************
! The flare includes the flare itself and the rectangular piece that extends down to the cathode.
! L1=0.639 nH, L2=0.924 nH, L1+L2=1.563 nH
! This section would be better modeled as MITLs as the lower portion of the feed could be 
!  emissive.
!

RLSeries  0.0    1.563E-9

!
! Extra stray L in the flare region 0.5 nH, just a WAG
!

RLSeries  0.0    0.5E-9

!
UFO VOUT
$V_vf_B
UFO IOUT
$I_vf_B
UFO POUT
$P_vf_B
UFO EOUT
$E_vf_B

!
!   *****************************   Constant Z MITLs   ********************************
! Z= 3.7 , length = 2.5 ns (Router = 89.65 cm gap=5.53 cm, Rinner=16.2 cm gap=1 cm)
! L=Zt - 9.25 nH
! I will divide the spacing between Router and Rinner into five segments of equal distance
!  and use the mid point of each segment as the circumference for the MITL model
! 14.69 cm long segments, midpoints - 82.305, 67.615, 52.925, 38.235, 23.545 
!
!MITL      Circum            Gap            Length-s       Impedance        Resolution       E-Turnon
MITL         5.63            5.08e-02        0.5E-09          3.7

UFO VOUT
$V_mitl1_out_B
UFO IOUT
$I_mitl1_out_B

MZFlow 3.7
UFO ICA
$Icath_mitl1_B
UFO IPL
$Iflow_mitl1_B
UFO ZOT
$Zflow_mitl1_B
               
MITL         4.219          4.17e-02        0.5E-09          3.7               

UFO VOUT
$V_mitl2_out_B
UFO IOUT
$I_mitl2_out_B

MITL         3.325          3.27e-02        0.5E-09          3.7               

UFO VOUT
$V_mitl3_out_B
UFO IOUT
$I_mitl3_out_B

MITL         2.402          2.36e-02        0.5E-09          3.7               

UFO VOUT
$V_mitl4_out_B
UFO IOUT
$I_mitl4_out_B

MITL         1.479          1.45e-02        0.5E-09          3.7

UFO VOUT
$V_mitl5_out_B
UFO IOUT
$I_mitl5_out_B              
UFO POUT
$P_mitl5_out_B
UFO EOUT
$E_mitl5_out_B

!
! Inductance of the disk - plate transition at 16.2 cm to 10.4 cm
!    Gap = 1 cm at this location, top and bottom 0.886 nH
!    Will need MITL calls here at some point.
!

RLSeries 0.0       0.886E-9

!
! Stray L in the PHC region 0.5 nH - just a WAG
! Should be Router = 10 cm, Rinner 6.5 cm, 1-cm gap, L = .862 nH
! This could be a MITL piece but I am treating this in the Zflow losses
!

RLSeries  1.0E-12    0.5E-9

UFO VOUT
$V_disk_out_B
UFO IOUT
$I_disk_out_B

!
!   *****************************  Convolute  ******************************
! Convolute diameter 6 inches = 15.24 cm diameter, 7.62 cm radius
!  Assume a 1-cm inner gap/2-cm outer gap for all convoute spacings, Post diameter - 1.59 cm
!  Convolute height = 1 cm + 1.25 cm + 1 cm + 1.25 cm + 1 cm + 1.25 cm + 1 cm = 7.75 cm
!  Divide by 12 posts = 1.37 nH (1.5 cm gap coax estimate)
! The Z51 inductance for B level was 1.89 nH. A 3-D E&M code would give the correct information
!
! In series only with B level

RLSeries 0.0       1.37E-9

!
! Attach A level
! Branch #2
!

ENDbranch

!   *****  Z-flow current loss immediately downstream of the convolute  ******
!
!   We assume the MITL system has a Z-flow impedance of 1.20 ohms for two levels:
!  The 1.2  here seems to be arbitrary. For shot Z51, the value was adusted to match data.
!  The losses could be half that of Z (single PHC vs. double PHC), in which case the
!   Zflow would be 0.6 
!

RCG     0.0001      1.00E-12
VARIABLE R1      POS-MODEL 
!  TSW   CURSW   TOPEN  ZFLOW  GSWMIN  GSWMAX  CBFLAG
   2E-9   1E2            2E-9      1.20        0.0001      10000         0

UFO IR1
$I_zfloss
UFO R1
$R_zfloss

!
!   *******************  Inner-MITL, coax, and pinch at t = 0  ********************
!   THE INNER MITL INDUCTANCE Disk from PHC
!   Router = 7.62 - .625 -1 = 6 cm, Rinner = 2.5 cm, gap = 0.5 cm
! We are treating this as a lumped L but it could be a MITL.
!

RLSeries   0.0       1.04E-9

!
! Extra stray L in the inner MITL region - just a WAG
!

RLSeries  0.0      0.25E-9

UFO VOUT
$V_in_coax

!
!   The lower coax INDUCTANCE Router = 2.5 cm, Rinner = 2 cm, height = 0.5 + 1.25 cm
!      this is to the base of the load
!

RLSeries 0.0       0.781E-9

UFO VOUT
$V_out_coax

!
!   Initial PRS Load Inductance 2 cm height, 2 cm wire array radius, 0.5 cm AK gap
!

RLSeries 0.0  0.89E-9

!     
!    *********   Time-dependent z-pinch model   ****************************
!
!   We choose a 2-cm initial radius, a 2-cm length, 1-mg mass, and a 20:1 convergence ratio.
! 
!                INITIAL R     LENGTH   TOTAL MASS    FINAL R
CYLFOIL      0.02             0.02             1.0e-6            0.001
!
!

UFO FRAD
$Rad_PRS
UFO FVEL
$Vel_PRS
UFO FKE
$E_kinetic_PRS
UFO VIN
$V_load
UFO IIN
$I_load
UFO EIN
$E_load
UFO PIN
$P_load
UFO L2
$L_load
UFO R2
$R-liner
UFO VR2
$V_liner
UFO PR2
$P_liner

!
!   ********   Tie it all back to ground   ********************************
!

RCG  1.0E-12  1.0E-12

!
! End Main Branch (Branch #1)
!
! Level 2 Branches
!
! Branch #2
! Note: all elements are in reverse order inside to outside
!

Branch

!
! L through the PHC region to the post center 0.5 nH -  just a WAG now
! Should be Router = 10 cm, Rinner 6.5 cm, 1-cm gap, L = .862 nH
! This could be a MITL piece but I am treating this in the Zflow losses
!

RLSeries  0.0    0.5E-9

UFO IIN
$I_mitl_A

!
! Inductance of the disk - plate transition at 16.2 cm to 10.4 cm
!    Gap = 1 cm at this location, top and bottom 0.886 nH
! Need to replace this with several MITL elements.
!

RLSeries 0.0       0.886E-9


!   *****************************   Constant Z MITLs   ********************************
! Z= 3.7 , length = 2.5 ns (Router = 89.65 cm gap=5.53 cm, Rinner=16.2 cm gap=1 cm)
! L=Zt - 9.25 nH
! I will divide the spacing between Router and Rinner into five segments of equal distance
!  and use the mid point of each segment as the circumference
! 14.69 cm long segments, midpoints - 82.305, 67.615, 52.925, 38.235, 23.545 
! Remember in the branch outputs and inputs are in reverse order
!
!MITL      Circum            Gap            Length-s       Impedance        Resolution       E-Turnon
MITL         1.479          1.45e-02        0.5E-09          3.7

UFO VIN
$V_mitl5_out_A               
UFO IIN
$P_mitl5_out_A
UFO EIN
$E_mitl5_out_A

MITL         2.402          2.36e-02        0.5E-09          3.7               

UFO VIN
$V_mitl4_out_A
UFO IIN
$I_mitl4_out_A

MITL         3.325          3.27e-02        0.5E-09          3.7               

UFO VIN
$V_mitl3_out_A
UFO IIN
$I_mitl3_out_A

MITL         4.219          4.17e-02        0.5E-09          3.7               

UFO VIN
$V_mitl2_out_A
UFO IIN
$I_mitl2_out_A

MITL         5.63            5.08e-02        0.5E-09          3.7

UFO VIN
$V_mitl1_out_A
UFO IIN
$I_mitl1_out_A
               
!
! Stray L in the flare region 0.5 nH - divide by two, just a WAG
!

RLSeries  1.0E-12    0.5E-9

!
UFO VIN
$V_vf_A
UFO IIN
$I_vf_A
UFO PIN
$P_vf_A
UFO EIN
$E_vf_A

!
!
!   **************************  Vacuum flares  *****************************
! The flare includes the flare itself and the piece that extends down to the cathode.
! L1=0.639 nH, L2=0.924 nH, L1+L2=1.563 nH
! Two vacuum flares in parallel - divide by 2
!

RLSeries  0.0    1.563E-9

!
!   **************************  First vacuum piece inside insulator  *****************************
!  Constant 13.35 cm height, Router = 1 m, Rinner = 0.975 m
! Inductance = 0.676 nH - divide by 2
!

RLSeries  0.0    0.676E-9

!
!   ***********************  Insulator stack  *****************************
! The water/vacuum interface Router=1.1 m, Rinner=1.0 m, height=13.35 cm (0.64-cm grading rings) 
!  Plastic height is 11.43 cm. L per side = 2.1788 nH
! Two stacks in parallel - divide L by 2
!

RLS  1.0E-12    2.1788E-9

!
UFO VIN
$V_stack_A
UFO IR2
$I_stack_A
UFO PIN
$P_stack_A
UFO EIN
$E_stack_A

!
!  ********* Water flare transition external to the insulator stack ****************
!  Router = 1.165 m , stack outer = 1.1 m, constant 13.35-cm gap, l = 1.96 ns
!  Zouter = 0.76 , Zinner = 0.81   Divide by 2X
!

TRLine LIN 1.96e-9 0.81 0.76

!
! Output Line (OL),  72 ns, 1.4  constant impedance
!  Divide by 2 for 2 modules
!

TRLine LIN 70e-09 .7 .7

UFO VIN
$V_OL_out_A
UFO IIN
$I_OL_out_A
UFO PIN
$P_OL_out_A
UFO EIN
$E_OL_out_A

TRLine EXP 2.29e-09 .7 2

UFO VOUT
$V_OL_in_A
UFO IOUT
$I_OL_in_A

!
! Line 2 water switches
! 7 output switches, 0.5 gap + switch inductance
!  Increase number of channels to four for four modules
!

RLSeries 10e9 5e-9
Var R2 Switch
!dielectric switchtime gap      pressure     nswitch  nchannels
H2O         400e-09    0.0127   1.0                    7               2

UFO IR2
$I_PFL_sw_A
UFO R2
$R_PFL_sw_A
UFO ER2
$E_PFL_sw_A
UFO QR2
$Q_PFL_sw_A

!
! Line 2, 72 ns, 1.4  constant impedance
!

TRLine EXP 2.29e-09 2 .7

UFO VIN
$V_PFL_out_A
UFO IIN
$I_PFL_out_A
UFO PIN
$P_PFL_out_A
UFO EIN
$E_PFL_out_A

TRLine LIN 68e-09 .7 .7
TRLine EXP 2.29e-09 .7 2

UFO VOUT
$V_PFL_in_A
UFO IOUT
$I_PFL_in_A

!
! CPL water switches
! 5 output switches, 4 gap + switch inductance
!  Increase number of channels for the four modules
!

RLSeries 10e9 5e-9
Var R2 Switch
!dielectric switchtime gap         pressure   nswitch  nchannels
H2O          310e-09     0.1016   1.0              5             2

UFO IR2
$I_CPL_sw_A
UFO R2
$R_CPL_sw_A
UFO ER2
$E_CPL_sw_A
UFO QR2
$Q_CPL_sw_A

TRLine EXP 2.29e-09 2  .7

!
! Line 1 (CPL), 60 ns, 1.4 , 42.85 nF
! Divide by 2 for 2 modules
!

UFO VIN
$V_CPL_out_A
UFO IIN
$I_CPL_out_A
UFO EIN
$E_CPL_out_A
UFO PIN
$P_CPL_out_A
UFO EIN
$E_CPL_out_A

TRLine LIN   56.0e-09   .7  .7
TRLine EXP 2.29e-09    .7   2

!
! Output Marx header inductance
! 100 nH per Marx divided by 2 here
!

RLSeries 0.00 50e-9

!
! Switch resistance - Martin Model and switch inductance - the total gap for a single
!   switch from DWGs is 0.53 (1.346 cm) gap and 93 psig air X15 = 20.19 cm
!
! Initial switch resistance was chosen to be higher than that printed in the first
! few time steps so as to appear monotonically decreasing in R plots
! A careful few runs showed that 10 G looked best. In any event by 1 ns all of the 
! resistance values are the same.
! 10 switches for 10 sub-Marxes, 2 channels for 2 modules
!  Divide inductance by 2 for 2 modules
!

RLSeries 10e9 25e-9
Var R2 Switch
!dielectric switchtime gap        pressure     nswitch  nchannels
AIR           0.0               0.2019  7.3                10           2
UFO IR2
$I_marx_A
UFO R2
$R_switch_A
UFO ER2
$E_switch_A
UFO QR2
$Q_switch_A

!
! Cap inductance, case & parasitic inductance, and ESR
! ESR = 0.195 for the total Marx (1.95  sub Marx/10)
! Divide R and L by four for the four modules
!

RLSeries 0.098 12.5e-8

!
! Marx capacitance and charge voltage
! X2 for two modules
!

RCGround 1e+12 200e-9
Initial VC1 3.0e6
UFO VC1
$V_marx_A
UFO EC1
$E_marx_A

!
! End branch #2
