PRE-CONCEPTUAL DESIGN OF THE Z-15 ACCELERATOR
!
!    Following Mazarakis, Spielman, Kim, and colleagues, the design assumes LTD-module drivers.
!
!    Rev 4 is based on Rev 3 with multi-disk feed and a better representation of the MITL power flow
!    The design presented below is a single-line model of the machine.
!    Rev 3 is a more accurate representation of the inductance in the
!    water and the vacuum
!
!
!
TIME-STEP          1.00E-12
RESOLUTION-TIME    100E-12
END-TIME           0.5E-6
NUMBER-PRINTS      5
EXECUTE-CYCLES     ALL
ECHO               YES
GRIDS              NO
MAX-POINTS         8001
DETAIL-PRINTS      FULL

!
!   *********   10 LTD modules Total   ****************************************
!
!    We begin with a model of 10 LTD modules, connected in parallel.
!
!    We assume each LTD module consists of 16 LTD cavities, connected in series.
!
!    We assume each cavity includes 22 LTD bricks, in parallel.
!
!    Each brick is assumed to have a 40-nF capacitance and a 160-nH inductance.
!    We assume a capacitor ESR of 0.13 Ω.
!    Ctot = 40nF*22*10/16 = 0.55 µF
!    Vtot = 85 kV * 2 * 16 = 2.72 MV
!    Ltot = 160 nH/22 * 16 / 10 = 11.64 nH
!    Rtot = (.13 Ω * 2 + 0.04)/22 * 16 / 10 = 21.81 mΩ
!
!    We use for this calculation the RLC-circuit model of an LTD system that was
!    developed by Mazarakis, Spielman, and colleagues.
!
!    We assume a single core loss resistance of 115 Ω per cavity.
!    Thus, the core loss for the entire machine is:
!    Rloss = 115 * 16 / 10 = 184 Ω
!
!    Note: the matched load per module is R = (1.7 / 22) * 16 = 1.24 Ω
!
!    We assume a total LTD-system capacitance of 0.55 uF:
! Divide C by 2 and multiple L,R by 2 for the split disk case
!
! ******** Main Branch **********
! Level B
!

BRANCH

RCG  1.00E12    0.275E-6
INITIAL VC1    2.72E6

!
!    We assume each LTD cavity is charged to +/-85 kV:
!

!
!    We assume the series resistance of the LTD system total is 21.81 milliohms,
!    and the total series inductance is 11.64 nH:
!

RLS   43.62E-3    23.28E-9

!
!    We assume the total shunt resistance due to the cores is 184 ohms:
!

RCG    368     1.0E-12

!
!   **************   5 coaxial water-transmission-lines   **************
!
!    We assume that each of the modules has a 54-ns coaxial water TL 
!
!    We also assume that at this point, the impedance of a single TL is 1.25 Ω. The total impedance
!    of the water line outputs is 0.250 ohms.
!    We will need to add the TL losses in the water at some point.
!

TRL LIN  54.0E-9  0.25

!
UFO VIN
$V_tr_in_B
UFO IIN
$I_tr_in_B
UFO PIN
$P_tr_in_B
UFO EIN
$E_tr_in_B

!
!   ********   5 coaxial to tri-plate water-transmission-lines   ********
!
!    We assume that each of the 5 modules has a 54-ns long convolution in the water TL 
!
!    We also assume that at this point, the impedance of a single TL is 1. 25 Ω. The impedance
!    at the system output is 0.250 ohms.
!

TRL LIN  54.0E-9  0.250

!
!   *************************  Water flares  ******************************
!
!    This is the section of the water line that increases if gap to match the insulator
!    height. It starts matched and nearly doubles
!

TRL LIN 5.96E-9  0.250  0.480

UFO VOUT
$V_wf_B
UFO IOUT
$I_wf_B
UFO POUT
$P_wf_B
UFO EOUT
$E_wf_B

!
!   ***********************  Water constant gap  ****************************
!
!    This is the section of the water line that is constant gap near the insulator.
!    Because this is the disk in the water, it is a slowly increasing inductance.
!

TRL LIN 1.0E-9  0.480  0.510

!
UFO VOUT
$V_wc_B
UFO IOUT
$I_wc_B
UFO POUT
$P_wc_B
UFO EOUTw
$E_wc_B

!
!
!   ***********************  Insulator stack  *****************************
!
! The water/vacuum interface Router=1.73 m, Rinner=1.6 m (10.5 ft), plastic height=9.525 cm
! 4, 2.38125-cm high (15/16" high) insulators and 3, 1/4” grading rings 
! (We could standardize on 2.5 cm exactly)
! 
!

RLS  1.0E-12    1.488E-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 stack  *****************
!  Constant Gap
!  Router=1.6 m, Rinner=1.55 m, total height=11.43 cm (plastic + grading rings)
! 

RLS  1.0E-12    0.7258E-9

!
!   **************************  Vacuum flares  *****************************
!
! Start of the flare Router=1.55 m with a gap of 11.43 cm
! End of the flare  Rinner=1.5105 m with a gap of 5.022 cm
! height=6.408, 1.99 Ω
! Use triangle L formula, vertex in
! Hold angle of 31.65° - the same as Z
!

RLS  1.0E-12    0.1647E-9

!
! Extra inductance due to the radius of the of the flare - wag
!

RLS  1.0E-12    0.1E-9

!
!   ***************** Constant Gap under Vacuum flares  ********************
!
! Router=1.55 m, Rinner=1.5105 m with a gap of 5.022 cm
!

RLS  1.0E-12    0.2593E-9

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

!
!   *****************************   Constant 2-Ω MITLs   ********************************
! Router=1.5105 m at a gap of ~5.03 cm, Rinner=0.30 at a gap of 1 cm
! 2 Ω, 4.03 ns long, L = Zt = 8.06 nH
! (Router Z is actually 1.3 m due to the 4" radius of the transition)
! (The outer gap is ~  Z Router gap @1.3 m of 4.3 cm (vertical))
!
! I will divide the spacing between Router and Rinner into 10 segments of equal distance
!  and use the mid point of each segment as the circumference for the MITL model.
! 12.1 cm long segments, (½ segment = 6.05 cm)
! midpoints - 144.95,132.85,120.75,108.65,96.55,84.45,72.35,60.25,48.15,36.05 cm
! circumference - 9.107,8.347,7.587,6.827,6.066,5.306,4.546,3.786 ,3.025 ,2.265 m
! 2-Ω gaps  -  4.835 ,4.464 , 4.028  ,  3.625 ,3.221,2.817,2.414, 2.01 ,1.606,1.203 cm
!
!MITL    Circum          Gap                Length-s         Impedance        Resolution       E-Turnon
MITL      9.107            4.835e-02     0.4036E-09    2.0                      0.025e-9

UFO VOUT
$V_mitl1_out_B
UFO IOUT
$I_mitl1_out_B
UFO CLOS
$I_mitl1_loss_B
UFO ALOS
$J_mitl1_loss_B

!MZFlow 2
!UFO ICA
!$Icath_mitl1_B
!UFO IPL
!$Iflow_mitl1_B
!UFO ZOT
!$Zflow_mitl1_B
               
MITL         8.347          4.464e-02        0.4036E-09          2.0                      0.025e-9               

UFO VOUT
$V_mitl2_out_B
UFO IOUT
$I_mitl2_out_B
UFO CLOS
$I_mitl2_loss_B
UFO ALOS
$J_mitl2_loss_B

MITL         7.587          4.028e-02        0.4036E-09          2.0                      0.025e-9               

UFO VOUT
$V_mitl3_out_B
UFO IOUT
$I_mitl3_out_B
UFO CLOS
$I_mitl3_loss_B
UFO ALOS
$J_mitl3_loss_B

MITL         6.827        3.625e-02       0.4036E-09          2.0                     0.025e-9               

UFO VOUT
$V_mitl4_out_B
UFO IOUT
$I_mitl4_out_B
UFO CLOS
$I_mitl4_loss_B
UFO ALOS
$J_mitl4_loss_B

MITL         6.066         3.221e-02        0.4036E-09          2.0                      0.025e-9

UFO VOUT
$V_mitl5_out_B
UFO IOUT
$I_mitl5_out_B
UFO CLOS
$I_mitl5_loss_B
UFO ALOS
$J_mitl5_loss_B

MITL         5.306         2.817e-02        0.4036E-09          2.0                      0.025e-9

UFO VOUT
$V_mitl6_out_B
UFO IOUT
$I_mitl6_out_B
UFO CLOS
$I_mitl6_loss_B
UFO ALOS
$J_mitl6_loss_B

MITL         4.546         2.414e-02        0.4036E-09         2.0                      0.025e-9

UFO VOUT
$V_mitl7_out_B
UFO IOUT
$I_mitl7_out_B
UFO CLOS
$I_mitl7_loss_B
UFO ALOS
$J_mitl7_loss_B

MITL        3.786         2.01e-02        0.4036E-09          2.0                      0.025e-9

UFO VOUT
$V_mitl8_out_B
UFO IOUT
$I_mitl8_out_B
UFO CLOS
$I_mitl8_loss_B
UFO ALOS
$J_mitl8_loss_B

MITL         3.025         1.606e-02        0.4036E-09          2.0                      0.025e-9

UFO VOUT
$V_mitl9_out_B
UFO IOUT
$I_mitl9_out_B
UFO CLOS
$I_mitl9_loss_B
UFO ALOS
$J_mitl9_loss_B

MITL         2.265         1.203e-02        0.4036E-09          2.0                     0.025e-9

UFO VOUT
$V_mitl10_out_B
UFO IOUT
$I_mitl10_out_B
UFO CLOS
$I_mitl10_los_B
UFO ALOS
$J_mitl10_los_B
        
UFO POUT
$P_mitl10_out_B
UFO EOUT
$E_mitl10_out_B

!
! *************************Constant Gap to the PHC ********************
!  From the output of the MITL to the middle of the PHC posts
!  Router= 0.30 m, Rinner= .0762 m, gap = 1 cm

RLSeries 0.0 2.741E-9

!
!   *****************************  Convolute  ******************************
! Use Z51 value for the B-level inductance
!

RLS 0.0       1.89E-9

UFO IIN
$I_mitl_B

!
! Attach Level A
! Branch #2
!

ENDbranch

!
!   *****  Z-flow current loss immediately downstream of the convolute  ******
!
!   We assume the MITL system has a Z-flow impedance of 1.25 ohms for two levels:
!  Z has 0.25 ohms, could lower the Z-flow parameter here if needed
!

RCG     0.0001      1.00E-12
VARIABLE R1      POS-MODEL 
!  TSW     CURSW   TOPEN  ZFLOW  GSWMIN  GSWMAX  CBFLAG
   2.0E-9   1.0E2       2.0E-9   1.25   0.0001   10000     0
!
UFO IR1
$I_zflowloss
UFO R1
$R_loss

!
!   **************  Inner-MITL, coax, and pinch at t = 0  ******************
!   Disk MITL PHC to inner disk
! Router = 7.62 cm, Rinner = 5.62 cm, gap = 1.0 cm

RLS 0.0       0.609E-9

!   The inner disk MITL OD inner disk to coax
!   Router = 5.62 cm, Rinner = 2.5 cm, gap = 0.5 cm (could go to smaller gap)
!

RLS 0.0       0.81E-9

UFO IR2
$I_inner_mitl
RCG 1e12 0.0
UFO VR1
$V_inner_mitl

!
! Extra inductance due to the details of the MITL near the coax - WAG
!

RLS 0.0       0.25E-9

!
!   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

UFO VOUT
$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

!     
!
!   ***************  Electrode-wall resistance  ****************************
! This is from Bill Stygar’s run deck and is likely not needed for a 10 MA driver.
! Deleting this makes no difference to the run.
!
!RLS 0.0 0.0
!VAR  R2  R2WALL
!
!  tstart   cyl_length_inner   cyl_length_outer   cyl_r_inner  cyl_r_outer
!
!   1.0e-7       0.0175              0.0325           0.02       0.025
!
! disk_upper_r_inner  disk_upper_r_outer  disk_lower_r_inner  disk_lower_r_outer
!
!        0.025               0.065              0.02               0.065
!
!UFO R2
!$RWALL
!
!    *********   Time-dependent z-pinch model   ****************************
!
!   We choose a 2-cm initial radius, a 2-cm length, 1.5-mg mass, and a 20:1 convergence ratio.
! 
!          INITIAL R     LENGTH   TOTAL MASS    FINAL R
CYLFOIL      0.02        0.02     1.5e-6        0.001
!
!
UFO FRAD
$RAD_load
!
UFO FVEL
$VEL_load
!
UFO FKE
$E_kinetic
!
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

!
! *************************Constant Gap to the PHC ********************
!  From the output of the MITL at r=30 cm to the middle of the PHC posts
!  Router = 0.15 m, Rinner = .0762 m, gap = 1 cm
!

RLSeries 0.0 2.741E-9

UFO IOUT
$I_mitl_A

!
!   *****************************   Constant 2-Ω MITLs   ********************************
! Router=1.5105 m at a gap of ~5.03 cm, Rinner=0.30 at a gap of 1 cm
! 2 Ω, 4.03 ns long, L = Zt = 8.06 nH
! (Router Z is actually 1.3 m due to the 4" radius of the transition)
! (The outer gap is ~  Z Router gap @1.3 m of 4.3 cm (vertical))
!
! I will divide the spacing between Router and Rinner into 10 segments of equal distance
!  and use the mid point of each segment as the circumference for the MITL model.
! 12.1 cm long segments, (½ segment = 6.05 cm)
! midpoints - 144.95,132.85,120.75,108.65,96.55,84.45,72.35,60.25,48.15,36.05 cm
! circumference - 9.107,8.347,7.587,6.827,6.066,5.306,4.546,3.786 ,3.025 ,2.265 m
! 2-Ω gaps  -  4.835 ,4.464 , 4.028  ,  3.625 ,3.221,2.817,2.414, 2.01 ,1.606,1.203 cm
!
!MITL    Circum          Gap                Length-s         Impedance        Resolution       E-Turnon
MITL         2.265         1.203e-02        0.4036E-09          2.0                     0.025e-9

UFO VIN
$V_mitl10_out_A
UFO IIN
$I_mitl10_out_A
UFO CLOS
$I_mitl10_los_A
UFO ALOS
$J_mitl10_los_A
        
UFO PIN
$P_mitl10_out_A
UFO EIN
$E_mitl10_out_A

MITL         3.025         1.606e-02        0.4036E-09          2.0                      0.025e-9

UFO VIN
$V_mitl9_out_A
UFO IIN
$I_mitl9_out_A
UFO CLOS
$I_mitl9_loss_A
UFO ALOS
$J_mitl9_loss_A

MITL        3.786         2.01e-02        0.4036E-09          2.0                      0.025e-9

UFO VIN
$V_mitl8_out_A
UFO IIN
$I_mitl8_out_A
UFO CLOS
$I_mitl8_loss_A
UFO ALOS
$J_mitl8_loss_A

MITL         4.546         2.414e-02        0.4036E-09         2.0                      0.025e-9

UFO VIN
$V_mitl7_out_A
UFO IIN
$I_mitl7_out_A
UFO CLOS
$I_mitl7_loss_A
UFO ALOS
$J_mitl7_loss_A

MITL         5.306         2.817e-02        0.4036E-09          2.0                      0.025e-9

UFO VIN
$V_mitl6_out_A
UFO IIN
$I_mitl6_out_A
UFO CLOS
$I_mitl6_loss_A
UFO ALOS
$J_mitl6_loss_A

MITL         6.066         3.221e-02        0.4036E-09          2.0                      0.025e-9

UFO VIN
$V_mitl5_out_A
UFO IIN
$I_mitl5_out_A
UFO CLOS
$I_mitl5_loss_A
UFO ALOS
$J_mitl5_loss_A

MITL         6.827        3.625e-02       0.4036E-09          2.0                     0.025e-9               

UFO VIN
$V_mitl4_out_A
UFO IIN
$I_mitl4_out_A
UFO CLOS
$I_mitl4_loss_A
UFO ALOS
$J_mitl4_loss_A

MITL         7.587          4.028e-02       0.4036E-09          2.0                      0.025e-9               

UFO VIN
$V_mitl3_out_A
UFO IIN
$I_mitl3_out_A
UFO CLOS
$I_mitl3_loss_A
UFO ALOS
$J_mitl3_loss_A

MITL         8.347          4.464e-02        0.4036E-09          2.0                      0.025e-9               

UFO VIN
$V_mitl2_out_A
UFO IIN
$I_mitl2_out_A
UFO CLOS
$I_mitl2_loss_A
UFO ALOS
$J_mitl2_loss_A

MITL      9.107            4.835e-02        0.4036E-09           2.0                      0.025e-9

UFO VIN
$V_mitl1_out_A
UFO IIN
$I_mitl1_out_A
UFO CLOS
$I_mitl1_loss_A
UFO ALOS
$J_mitl1_loss_A


!
!   ***************** Constant Gap under Vacuum flares  ********************
!
! Router=1.55 m, Rinner=1.51 m with a gap of 4.94 cm
!

RLS  1.0E-12    0.2583E-9

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

!
! Extra inductance due to the radius of the of the flare - wag
!

RLS  1.0E-12    0.1E-9

!
!   **************************  Vacuum flares  *****************************
!
! Start of the flare Router=1.55 m with a gap of 11.43 cm
! End of the flare  Rinner=1.51 m with a gap of 4.94 cm
! height=6.49, 1.96 Ω
! Use triangle L formula, vertex in
! Hold angle of 31.65° - the same as Z
!

RLS  1.0E-12    0.1689E-9

!
!   ***************  First Vacuum Piece Inside Insulator stack  *****************
!  Constant Gap
!  Router=1.6 m, Rinner=1.55 m, total height=11.43 cm (plastic + grading rings)
! 

RLS  1.0E-12    0.7258E-9

!
!
!   ***********************  Insulator stack  *****************************
!
! The water/vacuum interface Router=1.73 m, Rinner=1.6 m (10.5 ft), plastic height=9.525 cm
! 4, 2.38125-cm high (15/16" high) insulators and 3, 1/4” grading rings 
! (We could standardize on 2.5 cm exactly)
! 
!

RLS  1.0E-12    1.488E-9

UFO VIN
$V_stack_A
UFO IIN
$I_stack_A
UFO PIN
$P_stack_A
UFO EIN
$E_stack_A

!
!   ***********************  Water constant gap  ****************************
!
!    This is the section of the water line that is constant gap near the insulator.
!    Because this is the disk in the water, it is a slowly increasing inductance.
!

TRL LIN 1.0E-9  0.480  0.510

UFO VIN
$V_wc_A
UFO IIN
$I_wc_A
UFO PIN
$P_wc_A
UFO EIN
$E_wc_A

!
!   *************************  Water flares  ******************************
!
!    This is the section of the water line that increases if gap to match the insulator
!    height. It starts matched and nearly doubles
!

TRL LIN 5.96E-9  0.250  0.480

UFO VIN
$V_wf_A
UFO IIN
$I_wf_A
UFO PIN
$P_wf_A
UFO EIN
$E_wf_A

!
!   ********   5 coaxial to tri-plate water-transmission-lines   ********
!
!    We assume that each of the 5 modules has a 54-ns long convolution in the water TL 
!
!    We also assume that at this point, the impedance of a single TL is 1. 25 Ω. The impedance
!    at the system output is 0.250 ohms.
!

TRL LIN  54.0E-9  0.250

!
!   **************   5 coaxial water-transmission-lines   **************
!
!    We assume that each of the modules has a 54-ns coaxial water TL 
!
!    We also assume that at this point, the impedance of a single TL is 1.25 Ω. The total impedance
!    of the water line outputs is 0.250 ohms.
!    We will need to add the TL losses in the water at some point.
! output in and out are reversed in end Branches
!

TRL LIN  54.0E-9  0.25

!
UFO VOUT
$V_tr_in_A
UFO IOUT
$I_tr_in_A
UFO POUT
$P_tr_in_A
UFO EOUT
$E_tr_in_A

!
!    We assume the total shunt resistance due to the cores is 184 ohms:
!

RCG    368.0     1.0E-12

!
!    We assume the series resistance of the LTD system total is 21.81 milliohms,
!    and the total series inductance is 11.64 nH:
!

RLS   43.62E-3    23.28E-9

!
!   *********   10 LTD modules Total   ****************************************
!
!    We begin with a model of 10 LTD modules, connected in parallel.
!
!    We assume each LTD module consists of 16 LTD cavities, connected in series.
!
!    We assume each cavity includes 22 LTD bricks, in parallel.
!
!    Each brick is assumed to have a 40-nF capacitance and a 160-nH inductance.
!    We assume a capacitor ESR of 0.13 Ω.
!    Ctot = 40nF*22*10/16 = 0.55 µF
!    Vtot = 85 kV * 2 * 16 = 2.72 MV
!    Ltot = 160 nH/22 * 16 / 10 = 11.64 nH
!    Rtot = (.13 Ω * 2 + 0.04)/22 * 16 / 10 = 21.81 mΩ
!
!    We use for this calculation the RLC-circuit model of an LTD system that was
!    developed by Mazarakis, Spielman, and colleagues.
!
!    We assume a single core loss resistance of 115 Ω per cavity.
!    Thus, the core loss for the entire machine is:
!    Rloss = 115 * 16 / 10 = 184 Ω
!
!    Note: the matched load per module is R = (1.7 / 22) * 16 = 1.24 Ω
!
!    We assume a total LTD-system capacitance of 0.55 uF:
! Divide C by 2 and multiple L,R by 2 for the split disk case
!
! First element of Level A
!
!    We assume each LTD cavity is charged to +/-85 kV:
!

RCG  1.00E12    0.275E-6
INITIAL VC1    2.72E6

!
! End Branch #2
!