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 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
!
! Marx capacitance and charge voltage
! X4 for four modules
!
RCGround 1e+12 400e-9
Initial VC1 3.0e6
UFO VC1
$V_marx
UFO EC1
$E_marx
!
! 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 0.049 62.5e-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.
! Four channels for 4 modules
!  Divide inductance by four for 4 modules
!
RLSeries 10e9 12.5e-9
Var R2 Switch
!dielectric switchtime gap        pressure     nswitch  nchannels
AIR           0.0               0.2019  7.3                10           4
UFO IR2
$I_marx
UFO R2
$R_switch
UFO ER2
$E_switch
UFO QR2
$Q_switch
!
! Output Marx header inductance
!

RLSeries 0.00 25e-9

!
! Line 1 (CPL), 60 ns, 1.4 , 42.85 nF
! Divide by 4 for 4 modules
!

TRLine EXP 2.29e-09  1   .35
TRLine LIN 56.0e-09   .35 .35
TRLine EXP 2.29e-09 .35  1

UFO VOUT
$V_CPL_out
UFO IOUT
$I_CPL_out
UFO EOUT
$E_CPL_out
UFO POUT
$P_CPL_out
UFO EOUT
$E_CPL_out

!
! CPL water switches
! 5 output switches, 4 gap + switch inductance
!  Increase number of channels for the four modules
!
! Branch #2 Location

RLSeries 10e9 2.5e-9
Var R2 Switch
!dielectric switchtime gap         pressure   nswitch  nchannels
H2O          310e-09     0.1016   1.0              20             1

UFO IR2
$I_CPL_sw
UFO R2
$R_CPL_sw
UFO ER2
$E_CPL_sw
UFO QR2
$Q_CPL_sw
!TopBranch

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

TRLine EXP 2.29e-09 1 .35

UFO VIN
$V_PFL_in
UFO IIN
$I_PFL_in

TRLine LIN 68e-09 .35 .35
TRLine EXP 2.29e-09 .35 1

UFO VOUT
$V_PFL_out
UFO IOUT
$I_PFL_out
UFO POUT
$P_PFL_out
UFO EOUT
$E_PFL_out
!
! Line 2 water switches
! 7 output switches, 0.5 gap + switch inductance
!  Increase number of channels to four for four modules
!
! Branch #3 Location
RLSeries 10e9 2.5e-9
Var R2 Switch
!dielectric switchtime gap      pressure     nswitch  nchannels
H2O         400e-09    0.0127   1.0                    28               1
UFO IR2
$I_PFL_sw
UFO R2
$R_PFL_sw
UFO ER2
$E_PFL_sw
UFO QR2
$Q_PFL_sw
!TopBranch
!
! Output Line (OL),  72 ns, 1.4  constant impedance
!  Divide by four for four modules
!

TRLine EXP 2.29e-09 1 .35

UFO VIN
$V_OL_in
UFO IIN
$I_OL_in

TRLine LIN 70e-09 .35 .35

UFO VOUT
$V_OL_out
UFO IOUT
$I_OL_out
UFO POUT
$P_OL_out
UFO EOUT
$E_OL_out
!
!  ********* 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 0.38 0.405

!
!   ***********************  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    1.09E-9

!
UFO VOUT
$V_stack
UFO IOUT
$I_stack
UFO POUT
$P_stack
UFO EOUT
$E_stack
!
!   **************************  First vacuum piece inside insulator  *****************************
!  Constant 13.35 cm height, Router = 1 m, Rinner = 0.975 m
! Inductance = 0.676 nH - divide by 2
!

RLS  1.0E-12    0.338E-9

!
!
!   **************************  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
!

RLS  1.0E-12    0.78E-9

!
! Extra stray L in the flare region - divide by two, just a WAG
!

RLS  1.0E-12    0.25E-9

!
UFO VOUT
$V_vf
UFO IOUT
$I_vf
UFO POUT
$P_vf
UFO EOUT
$E_vf
!
!   *****************************   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 - Divide Z by 2 for this calculation.
! Note: This is the vacuum impedance without vacuum electron flow
! We should use the MITL model in Screamer.
!

TRLine LIN 2.5e-09 1.85 1.85

!
UFO VIN
$V_mitls_in
UFO IIN
$I_mitls_in
UFO VOUT
$V_mitls_out
UFO IOUT
$I_mitls_out
UFO POUT
$P_mitls_out
UFO EOUT
$E_mitls_out
!
! Extra inductance of the disk - plate transition at 16.2 cm to 10.4 cm
!    Gap = 1 cm at this location, top and bottom - Divide by 2
!

RLS 0.0       0.443E-9

!
! Extra stray L in the disk/PHC region - divide by two, just a WAG
!

RLS  1.0E-12    0.25E-9

!
!   *****************************  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) - Divide by 2
! The Z51 inductance for B level was 1.89 nH. A 3-D E&M code would give the correct information
!

RLS 0.0       0.6850E-9

!   *****  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:
!

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
!

RLS   0.0       1.04E-9

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

RLS  0.0      0.25E-9

!
! Location for a voltage probe
!

RCG 1e12 0.0

UFO VR1
$V_in_mitl

!
!   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
!

RLS 0.0       0.781E-9

!
! Location for a voltage probe
!

RCG 1e12 0.0

UFO VR1
$V_coax

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

RLS 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
!Branch
!RCGround 1.0e12 250.0e-12
!
! End branch #2
!
! Branch #3
!Branch
!RCGround 1.0e12 100.0e-12
!
! End branch #3
!
