tfcoil_variables Module

external case area per coil (inboard leg) (m2)

external case area per coil (outboard leg) (m2)

area of the cable conduit (m2)

Winding pack conductor area [m2] Does not include the area of voids and central helium channel

Cable space area (per turn) [m2] Includes the area of voids and central helium channel

single turn insulation area (m2)

winding pack turn insulation area per coil (m2)

Allowable maximum shear stress (Tresca criterion) in TF coil case (Pa)

Allowable maximum shear stress (Tresca criterion) in TF coil conduit (Pa)

Allowable Tresca stress in TF coil structural material (Pa)

outboard TF leg area (m2)

winding pack structure area (m2)

winding pack void (He coolant) area (m2)

winding pack He coil area (m2)

upper critical field (T) for Nb3Sn superconductor at zero temperature and strain (i_tf_sc_mat=4, =bc20m)

mean peak field at TF coil (T)

peak field at TF conductor with ripple (T)

case strain

inboard TF coil case plasma side thickness (m) (calculated for stellarators)

inboard TF coil case plasma side thickness as a fraction of tfcth

logical switch to make casthi a fraction of TF coil thickness (casthi_fraction)

inboard TF coil sidewall case thickness (m) (calculated for stellarators)

inboard TF coil sidewall case thickness as a fraction of tftort

logical switch to make casths a fraction of TF coil thickness (casths_fraction)

Conductor (cable + steel conduit) area averaged dimension [m]

TF coil turn edge length including turn insulation [m] If the turn is not a square (i_tf_turns_integer = 1) a squared turn of equivelent size is use to calculated this quantity If the t_turn_tf is non zero, cpttf is calculated

Boolean switch to activated when the user set the TF coil turn dimensions Not an input

f-value for TF turn edge length constraint If the turn is not a square (i_tf_turns_integer = 1) a squared turn of equivelent size is use for this constraint iteration variable ixc = 175 constraint equation icc = 86

TF turn edge length including turn insulation upper limit [m] If the turn is not a square (i_tf_turns_integer = 1) a squared turn of equivelent size is use for this constraint constraint equation icc = 86

TF coil superconducting cable squared/rounded dimensions [m] If the turn is not a square (i_tf_turns_integer = 1) a squared cable of equivelent size is use to calculated this quantity If the t_cable_tf is non zero, cpttf is calculated

Boolean switch to activated when the user set the TF coil cable dimensions Not an input

Area of space inside conductor (m2)

TF outboard leg current density (A/m2) (resistive coils only)

centering force on inboard leg (per coil) (N/m)

length of TF coil inboard leg ('centrepost') (i_tf_sup = 1)

TF coil current per turn (A). (calculated for stellarators) (calculated for integer-turn TF coils i_tf_turns_integer=1) (iteration variable 60)

Max TF coil current per turn [A]. (for stellarators and i_tf_turns_integer=1) (constraint equation 77)

density of coil case (kg/m3)

density of superconductor type given by i_tf_sc_mat/isumatoh/isumatpf (kg/m3)

density of conduit + ground-wall insulation (kg/m3)

diameter of central helium channel in TF winding (m)

total stored energy in the toroidal field (GJ)

upper critical field of GL_nbti

critical temperature of GL_nbti

Maximal (WP averaged) force density in TF coils at 1 point. (MN/m3)

copper fraction of cable conductor (TF coils) (iteration variable 59)

technology adjustment factor for critical current density fit for isumat..=2 Bi-2212 superconductor, to describe the level of technology assumed (i.e. to account for stress, fatigue, radiation, AC losses, joints or manufacturing variations; 1.0 would be very optimistic)

Radial strain in insulator

Switch for the TF coil stress model 0 : Generalized plane strain formulation, Issues #977 and #991, O(n^3) 1 : Old plane stress model (only for SC) 2 : Axisymmetric extended plane strain, Issues #1414 and #998, O(n)

Switch for TF coil conduit Tresca stress criterion: 0 : Tresca (no adjustment); 1 : Tresca with CEA adjustment factors (radial+2%, vertical+60%)

Switch for TF WP geometry selection 0 : Rectangular geometry 1 : Double rectangular geometry 2 : Trapezoidal geometry (constant lateral casing thickness) Default setting for backward compatibility if i_tf_turns_integer = 0 : Double rectangular if i_tf_turns_integer = 1 : Rectangular

Switch for TF case geometry selection 0 : Circular front case (ITER design) 1 : Straight front case

Switch for TF coil integer/non-integer turns: 0 : non-integer turns 1 : integer turns

Switch for superconductor material in TF coils:

• =1 ITER Nb3Sn critical surface model with standard ITER parameters
• =2 Bi-2212 high temperature superconductor (range of validity T < 20K, adjusted field b < 104 T, B > 6 T)
• =3 NbTi
• =4 ITER Nb3Sn model with user-specified parameters
• =5 WST Nb3Sn parameterisation
• =6 REBCO HTS tape in CroCo strand
• =7 Durham Ginzburg-Landau critical surface model for Nb-Ti
• =8 Durham Ginzburg-Landau critical surface model for REBCO
• =9 Hazelton experimental data + Zhai conceptual model for REBCO

Switch for TF coil conductor model:

• =0 copper
• =1 superconductor
• =2 Cryogenic aluminium

Switch for TF coil toroidal shape:

• =0 Default value : Picture frame coil for TART / PROCESS D-shape for non itart
• =1 PROCESS D-shape : parametrise with 2 arcs
• =2 Picture frame coils

Switch for the behavior of the TF coil conductor elastic axial properties

• =0 Young's modulus is set to zero, and the conductor is not considered in the stress calculation. This corresponds to the case that the conductor is much less stiff than the conduit, or the case that the conductor is prevented (isolated) from taking axial loads.
• =1 Elastic properties are set by user input, using the variable eyoung_cond_axial
• =2 Elastic properties are set to reasonable defaults taking into account the superconducting material i_tf_sc_mat

Switch for the behavior of the elastic properties of the TF coil conductorin the transverse direction. Only active if i_tf_cond_eyoung_axial == 2

• =0 Cable not potted in solder. Transverse Young's modulus set to zero.
• =1 Cable potted in solder. If i_tf_cond_eyoung_axial == 2, the transverse Young's modulus of the conductor is equal to the axial, which is set to a sensible material-dependent default.

Number of pancakes in TF coil. Only used if i_tf_turns_integer=1

Number of layers in TF coil. Only used if i_tf_turns_integer=1

Size of the arrays per layers storing the radial dependent stress quantities (stresses, strain displacement etc..)

Switch for TF inboard suport structure design:

Default setting for backward compatibility - if copper resistive TF (i_tf_sup = 0) : Free standing TF without bucking structure - if Superconducting TF (i_tf_sup = 1) : Free standing TF with a steel casing - if aluminium TF (i_tf_sup = 2) : Free standing TF with a bucking structure Rem : the case is a bucking structure - =0 : Free standing TF without case/bucking cyliner (only a conductor layer) - =1 : Free standing TF with a case/bucking cylinder made of - if copper resistive TF (i_tf_sup = 0) : used defined bucking cylinder - if Superconducting TF (i_tf_sup = 1) : Steel casing - if aluminium resisitive TF (i_tf_sup = 2) : used defined bucking cylinder - =2 : The TF is in contact with the CS : "bucked and wedged design" Fast version : thin TF-CS interface neglected in the stress calculations (3 layers) The CS is frictionally decoupled from the TF, does not carry axial tension - =3 : The TF is in contact with the CS : "bucked and wedged design" Full version : thin TF-CS Kapton interface introduced in the stress calculations (4 layers) The CS and kaptop are frictionally decoupled from the TF, do not carry axial tension

Number of layers of different stress properties in the WP. If n_tf_graded_layers > 1, a graded coil is condidered

Number of layers considered for the inboard TF stress calculations set in initial.f90 from i_tf_bucking and n_tf_graded_layers

Maximum number of layers that can be considered in the TF coil composited/smeared stress analysis. This is the layers of one turn, not the entire WP. Default: 5. void, conductor, copper, conduit, insulation.

bussing current density (A/m2)

j_crit_str : superconductor strand critical current density under operating conditions (A/m2). Necessary for the cost calculation in $/kAm

j_crit_str_pf_0 : superconductor strand critical current density at 6 T and 4.2 K (A/m2) Necessary for the cost calculation in $/kAm

critical current density for winding pack (A/m2)

allowable TF coil winding pack current density, for dump temperature rise protection (A/m2)

winding pack engineering current density (A/m2)

Overall current density in TF coil inboard legs midplane (A/m2) Rem SK : Not used in tfcoil to set the current any more. Should not be used as iteration variable 12 any more. It is now calculated.

Insulator Young's modulus [Pa]. Default value (1.0D8) setup the following values - SC TF, eyoung_ins = 20 Gpa (default value from DDD11-2 v2 2 (2009)) - Al TF, eyoung_ins = 2.5 GPa (Kapton polymer)

Steel case Young's modulus (Pa) (default value from DDD11-2 v2 2 (2009))

SC TF coil conductor Young's modulus in the parallel (along the wire/tape) direction [Pa] Set by user input only if i_tf_cond_eyoung_axial == 1; otherwise set by the behavior of that switch.

SC TF coil conductor Young's modulus in the transverse direction [Pa] Set by user input only if i_tf_cond_eyoung_axial == 1; otherwise set by the behavior of that switch.

Resistive TF magnets bucking cylinder young modulus (Pa)

Copper young modulus. Default value taken from wikipedia

Aluminium young modulus. Default value taken from wikipedia

Steel Poisson's ratio, Source : https://www.engineeringtoolbox.com/metals-poissons-ratio-d_1268.html

Copper Poisson's ratio. Source : https://www.engineeringtoolbox.com/poissons-ratio-d_1224.html

Aluminium Poisson's ratio. Source : https://www.engineeringtoolbox.com/poissons-ratio-d_1224.html

Insulation Poisson's ratio. Default: Kapton. Source : DuPont™ Kapton® HN datasheet.

SC TF coil conductor Poisson's ratio in the parallel-transverse direction

SC TF coil conductor Poisson's ratio in the transverse-transverse direction

Radius of maximum TF B-field (m)

TF coil leg resistance (ohm)

Minimal distance between two toroidal coils. (m)

F-value for minimum tftort (constraint equation 82)

aximum allowable toroidal field ripple amplitude at plasma edge (%)

peak/average toroidal field ripple at plasma edge (%)

total (summed) current in TF coils (A)

Size of the radial distribution arrays per layers used for stress, strain and displacement distibution

Array refining the radii of the stress calculations arrays

TF Inboard leg radial stress in steel r distribution at mid-plane [Pa]

TF Inboard leg tangential stress in steel r distribution at mid-plane [Pa]

TF coil radial deflection (displacement) radial distribution [m]

TF Inboard leg vertical tensile stress in steel at mid-plane [Pa]

TF Inboard leg Von-Mises stress in steel r distribution at mid-plane [Pa]

TF Inboard leg maximum shear stress (Tresca criterion) in steel r distribution at mid-plane [Pa]

Maximum shear stress (Tresca criterion) in CS structures at CS flux swing [Pa]:

• If superconducting CS (ipfres = 0): turn steel conduits stress
• If resistive CS (ipfres = 1): copper conductor stress

Quantity only computed for bucked and wedged design (i_tf_bucking >= 2) Def : CS Flux swing, instant when the current changes sign in CS (null current)

Maximum shear stress (Tresca criterion) in TF casing steel structures (Pa)

Residual manufacturing strain in CS superconductor material

Residual manufacturing strain in PF superconductor material

Residual manufacturing strain in TF superconductor material If i_str_wp == 0, used to compute the critical surface. Otherwise, the self-consistent winding pack str_wp is used.

Axial (vertical) strain in the TF coil winding pack found by self-consistent stress/strain calculation. if i_str_wp == 1, used to compute the critical surface. Otherwise, the input value str_tf_con_res is used. Constrain the absolute value using constraint equation 88 You can't have constraint 88 and i_str_wp = 0 at the same time

Maximum allowed absolute value of the strain in the TF coil (Constraint equation 88)

Switch for the behavior of the TF strain used to compute the strain-dependent critical surface:

• =0 str_tf_con_res is used
• =1 str_wp is used

switch for TF coil quench model (Only applies to REBCO magnet at present, issue #522):

• ='exponential' exponential quench with constant discharge resistor
• ='linear' quench with constant voltage

Time at which TF quench is detected (s)

critical temperature (K) for superconductor at zero field and strain (i_tf_sc_mat=4, =tc0m)

fast discharge time for TF coil in event of quench (s) (iteration variable 56)

For REBCO model, meaning depends on quench_model:

• exponential quench : e-folding time (s)`
• linear quench : discharge time (s)

Area of inboard midplane TF legs (m2)

TF coil bus length (m)

TF coil bus mass (kg)

available DC power for charging the TF coils (kW)

Peak power per TF power supply (MW)

Peak resistive TF coil inboard leg power (MW)

TF joints resistive power losses (MW)

surface area of toroidal shells covering TF coils (m2)

TF coil half-width - inner bore (m)

TF coil inductance (H)

TF coil WP insertion gap (m)

TF coil outboard leg resistive power (MW)

TF coil inboard leg resistivity [Ohm-m]. If itart=0, this variable is the average resistivity over the whole magnet

Resistivity of a TF coil leg (Ohm-m)

Resistivity of a TF coil bus (Ohm-m). Default value takes the same res as the leg one

Centrepost resistivity enhancement factor. For itart=0, this factor is used for the whole magnet

Ouboard legs resistivity enhancement factor. Only used for itart=1.

Switch for CP demoutable joints type -= 0 : Clampled joints -= 1 : Sliding joints Default value (-1) choses : Sliding joints for resistive magnets (i_tf_sup = 0, 2) Clampled joints for superconducting magents (i_tf_sup = 1)

TF joints surfacic resistivity [ohm.m]. Feldmetal joints assumed.

Number of contact per turn

Number of joints Ex: n_tf_joints = 2 for top and bottom CP joints

TF sliding joints contact pad width [m]

Calculated TF joints resistive power losses [W]

TF coil circumference (m)

TF cryoplant efficiency (compared to pefect Carnot cycle). Using -1 set the default value depending on magnet technology:

• i_tf_sup = 1 : SC magnet, eff_tf_cryo = 0.13 (ITER design)
• i_tf_sup = 2 : Cryo-aluminium, eff_tf_cryo = 0.4

Number of TF coils (default = 50 for stellarators). Number of TF coils outer legs for ST

TF coil half-width - outer bore (m)

area of the inboard TF coil legs (m2)

area of the outboard TF coil legs (m2)

peak helium coolant temperature in TF coils and PF coils (K)

TF coil toroidal thickness (m)

conduit insulation thickness (m)

Additional insulation thickness between layers (m)

inboard TF coil case outer (non-plasma side) thickness (m) (iteration variable 57) (calculated for stellarators)

radial thickness of winding pack (m) (iteration variable 140) (issue #514)

TF coil conduit case thickness (m) (iteration variable 58)

Thickness of the ground insulation layer surrounding (m) - Superconductor TF (i_tf_sup == 1) : The TF coil Winding packs - Resistive magnets (i_tf_sup /= 1) : The TF coil wedges Rem : Thickness calculated for stellarators.

minimum allowable temperature margin : TF coils (K)

minimum allowable temperature margin : CS (K)

minimum allowable temperature margin : TFC AND CS (K)

temperature margin (K)

TF coil temperature margin (K)

maximum temp rise during a quench for protection (K)

CroCo strand: maximum permitted temp during a quench (K)

CroCo strand: Actual temp reached during a quench (K)

coil temperature for cryogenic plant power calculation (K)

number of turns per TF coil

max voltage across TF coil during quench (kV) (iteration variable 52)

vertical tension on inboard leg/coil (N)

Fraction of the total vertical force taken by the TF inboard leg tension Not used for resistive itart=1 (sliding joints)

Vertical tension on outboard leg/coil (N)

coolant fraction of TFC 'cable' (i_tf_sup=1), or of TFC leg (i_tf_ssup=0)

volume of each TF coil outboard leg (m3)

TF coil voltage for resistive coil including bus (kV)

voltage across a TF coil during quench (kV)

mass per coil of external case (kg)

TF coil conductor mass per coil (kg/coil). For itart=1, coil is return limb plus centrepost/n_tf

copper mass in TF coil conductor (kg/coil). For itart=1, coil is return limb plus centrepost/n_tf

Aluminium mass in TF coil conductor (kg/coil). For itart=1, coil is return limb plus centrepost/n_tf

conduit insulation mass in TF coil conductor (kg/coil)

superconductor mass in TF coil cable (kg/coil)

steel conduit mass in TF coil conductor (kg/coil)

mass of ground-wall insulation layer per coil (kg/coil)

total mass of the TF coils (kg)

width of first step of winding pack (m)

width of second step of winding pack (m)

angle of arc i (rad)

radius of arc i (m)

x location of arc point i on surface (m)

x location of arc centre i (m)

y location of arc point i on surface (m)

y location of arc centre i (m)

Horizontal radius of inside edge of TF coil (m)

Vertical radius of inside edge of TF coil (m)

centrepost taper maximum radius adjustment (m)

centrepost taper height adjustment (m)

centrepost coolant pump efficiency

coolant fraction of TF coil inboard legs (iteration variable 23)

coolant fraction of TF coil outboard legs

Centrepost cooling area toroidal cross-section (constant over the whole CP)

number of centrepost coolant tubes

centrepost coolant pump power (W)

resistive power in the centrepost (itart=1) [W]. If itart=0, this variable is the ressitive power on the whole magnet

Summed resistive power in the TF coil legs [W]. Remain 0 if itart=0.

maximum peak centrepost temperature (K) (constraint equation 44)

average radius of coolant channel (m) (iteration variable 69)

centrepost coolant inlet temperature (K)

inlet / outlet TF coil coolant temperature rise (K)

Average temperature of centrepost called CP (K). Only used for resistive coils to compute the resisitive heating. Must be an iteration variable for ST (itart=1) (iteration variable 20)

Computed centrepost average temperature (K) (for consistency)

Average temperature of the TF outboard legs [K]. If tlegav=-1.0, the ouboard legs and CP temperatures are the same. Fixed for now, should use a contraints eq like tcpav

peak centrepost temperature (K)

inlet centrepost coolant flow speed at midplane (m/s) (iteration variable 70)

Exact conductor volume in the centrepost (m3)

mass of TF coil inboard legs (kg)

mass of the TF coil legs (kg)

Cryo cooling requirement at helium temp 4.5K (kW)

The angle of the outboard arc forming the TF coil current center line [deg]

The angle of the outboard arc forming the Vacuum Vessel current center line [deg]

The allowable peak maximum shear stress in the vacuum vessel due to quench and fast discharge of the TF coils [Pa]