pfcoil_variables Module

maximum number of groups of PF coils

maximum number of PF coils in a given group

maximum number of points across the midplane of the plasma at which the field from the PF coils is fixed

maximum number of fixed current PF coils

maximum total number of coils across all groups

new variable to include 2 additional circuits: plasma and central solenoid

smoothing parameter used in PF coil current calculation at the beginning of pulse (BoP)

allowable hoop stress in Central Solenoid structural material (Pa)

Switch for CS stress calculation:

• =0 Hoop stress only
• =1 Hoop + Axial stress

Central solenoid vertical cross-sectional area (m2)

Central solenoid (OH) trun cross-sectional area (m2)

central solenoid conductor+void area with area of steel subtracted (m2)

maximum field in central solenoid at end of flat-top (EoF) (T)

maximum field in central solenoid at beginning of pulse (T)

peak field at coil i (T)

PF group current array, flux-swing cancellation current (MA) Input if i_pf_current=0, computed otherwise

PF group current array, equilibrium current (MA) Input if i_pf_current=0, computed otherwise

Central solenoid overall current density at beginning of pulse (A/m2)

Central solenoid overall current density at end of flat-top (A/m2) (iteration variable 37) (sweep variable 62)

current per turn in coil i at time j (A)

peak current per turn input for PF coil i (A)

PF coil current array, at beginning of pulse (MA) Indexed by coil number, not group number

PF coil current array, at flat top (MA) Indexed by coil number, not group number

PF coil current array, at end of pulse (MA) Indexed by coil number, not group number

Efficiency of transfer of PF stored energy into or out of storage.

ratio of central solenoid overall current density at beginning of flat-top / end of flat-top

ratio of central solenoid overall current density at beginning of pulse / end of flat-top (iteration variable 41)

copper fraction of strand in central solenoid

copper fraction of cable conductor (PF coils)

F-value for constraint equation 51

Switch for location of PF coil group i:

• =1 PF coil on top of central solenoid (flux ramp only)
• =2 PF coil on top of TF coil (flux ramp only)
• =3 PF coil outside of TF coil (equilibrium coil)
• =4 PF coil, general location (equilibrium coil)

switch for PF & CS coil conductor type:

• =0 superconducting PF coils
• =1 resistive PF coils

total sum of I x turns x radius for all PF coils and CS (Am)

switch for superconductor material in central solenoid:

• =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 superconductor material in PF 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

superconductor strand critical current density under operating conditions in central solenoid (A/m2). Necessary for the cost calculation in $/kA m

superconductor strand critical current density under operating conditions in PF coils (A/m2). Necessary for the cost calculation in $/kA m

Switch for controlling the current of the PF coils:

• =0 Input via the variables c_pf_cs_coil_pulse_start_ma, c_pf_cs_coil_flat_top_ma, c_pf_cs_coil_pulse_end_ma
• =1 SVD targets zero field across midplane (flux swing coils) and the correct vertical field at the plasma center (equilibrium coils)

Switch for the placement of Location 3 (outboard) PF coils when the TF coils are superconducting (i_tf_sup = 1)

• =0 (Default) Outboard PF coils follow TF shape in an ellipsoidal winding surface
• =1 Outboard PF coils all have same radius, cylindrical winding surface

central solenoid superconductor critical current density (A/m2) at beginning-of-pulse

central solenoid superconductor critical current density (A/m2) at end-of-flattop

central solenoid cable critical current density (A/m2) at beginning-of-pulse

central solenoid cable critical current density (A/m2) at end-of-flattop

number of PF circuits (including central solenoid and plasma)

number of PF coils in group j

number of filaments the top and bottom of the central solenoid should be broken into during scaling (5 - 10 is good)

number of groups of PF coils. Symmetric coil pairs should all be in the same group

number of PF coils (excluding the central solenoid) + 1

Central solenoid height / TF coil internal height

central solenoid steel fraction (iteration variable 122)

Ratio of permissible PF coil conductor current density to critical conductor current density based on short-sample DC measurements

steel case thickness for PF coil i (m)

PF coil resistivity (if i_pf_conductor=1) (Ohm-m)

Resistivity of CS and PF coil bus bars (irrespective of whether the coils themselves are superconducting or resistive) (Ohm-m)

mass of heaviest PF coil (tonnes)

radius of largest PF coil (m)

Total mean wall plug power dissipated in PFC and CS power supplies (MW) (issue #713)

central solenoid resistive power during flattop (W)

total PF coil resistive losses during flattop (W)

inner radius of coil i (m)

outer radius of coil i (m)

peak current in coil i (MA-turns)

average winding pack current density of PF coil i (A/m2) at time of peak current in that coil (calculated for i_pf_location=1 coils)

allowable central solenoid current density at end of flat-top (A/m2)

allowable central solenoid current density at beginning of pulse (A/m2)

allowable winding pack current density of PF coil i (A/m2)

radius to the centre of the central solenoid (m)

radial distance (m) from outboard TF coil leg to centre of i_pf_location=3 PF coils

radius of PF coil i (m)

offset (m) of radial position of i_pf_location=1 PF coils from being directly above the central solenoid

offset (m) of radial position of i_pf_location=2 PF coils from being at rmajor (offset = rpf2triangrminor)

PF coil radial positioning adjuster:

• for groups j with i_pf_location(j) = 1; rref(j) is ignored
• for groups j with i_pf_location(j) = 2; rref(j) is ignored
• for groups j with i_pf_location(j) = 3; rref(j) is ignored
• for groups j with i_pf_location(j) = 4; rref(j) is radius of the coil in units of minor radii from the major radius (r = rmajor + rref*rminor)

Maximum shear stress (Tresca criterion) coils/central solenoid [MPa]

maximum permissible tensile stress (MPa) in steel coil cases for superconducting PF coils (i_pf_conductor=0)

fraction of JxB hoop force supported by steel case for superconducting PF coils (i_pf_conductor=0)

mutual inductance matrix (H)

Central solenoid temperature margin (K)

number of turns in PF coil i

winding pack void fraction of PF coil i for coolant

void fraction of central solenoid conductor for coolant

total flux swing available for burn (Wb)

flux swing from PF coils for burn (Wb)

flux swing from PF coils for startup (Wb)

total flux swing from PF coils (Wb)

total flux swing from the central solenoid (Wb)

central solenoid flux swing for burn (Wb)

central solenoid flux swing for startup (Wb)

total flux swing for startup (constraint eqn 51 to enforce vs_cs_pf_total_ramp=vs_plasma_res_ramp+vs_plasma_ind_ramp) (Wb)

total flux swing for pulse (Wb)

used in current waveform of PF coils/central solenoid

total mass of the PF coil conductor (kg)

total mass of the PF coil structure (kg)

conductor mass for PF coil i (kg)

structure mass for PF coil i (kg)

upper point of PF coil i (m)

lower point of PF coil i (m)

z (height) location of PF coil i (m)

PF coil vertical positioning adjuster:

• for groups j with i_pf_location(j) = 1; zref(j) is ignored
• for groups j with i_pf_location(j) = 2 AND itart=1 (only); zref(j) is distance of centre of PF coil from inside edge of TF coil (remember that PF coils for STs lie within the TF coil)
• for groups j with i_pf_location(j) = 3; zref(j) = ratio of height of coil group j to plasma minor radius

Central solenoid max field limit [T]

F-value for CS mmax field (cons. 79, itvar 149)

Ratio of CS coil turn conduit length to depth

Length of CS of CS coil turn conduit

Depth/width of CS of CS coil turn conduit

Length of CS of CS coil turn conduit length

Length of CS of CS coil turn conduit length