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PF Coil Model

The poloidal field (PF) coils are used initially to cancel the vertical field produced at the centre of the plasma by the central solenoid during start-up, and then to maintain the plasma position and shape during the flat-top period.

Positioning

The positions and sizes of te PF coils are partly input, and partly calculated after consideration of the required currents and allowable current density.

The PF coil locations are controlled using a set of switches stored in array i_pf_location[]. The coils are (usually) organised into groups containing two PF coils placed symmetrically above and below the midplane, and each group j has an element i_pf_location(j) assigned to it. Input parameter n_pf_coil_groups should be set to the number of groups, and n_pf_coils_in_group(j) should be assigned the number of coils in each group - which should be 2 in each case.

The values for dr_pf_cs_middle_offset, rpf2, zref(j) and dr_pf_tf_outboard_out_offset should be adjusted by the user to locate the PF coils accurately.

For PF coils going to be placed outside the TF coils the key radius is defined as:

\overbrace{R_{\text{PF, outside-TF}}}^{\texttt{r_pf_outside_tf_midplane}} = \overbrace{R_{\text{TF,outboard-out}}}^{\texttt{r_tf_outboard_out}} + \overbrace{dR_{\text{PF,TF-offset}}}^{\texttt{dr_tf_outboard_out_offset}}

The four possible values of i_pf_location(j) correspond to the following PF coil positions:

Above the central solenoid (one group only) | place_pf_above_cs()

  • i_pf_location(j) = 1;

    R = \overbrace{R_{\text{CS,middle}}}^{\texttt{r_cs_middle}} + \overbrace{dR_{\text{offset}}}^{\texttt{dr_pf_cs_middle_offset}}
    Z = \pm \ \overbrace{Z_{\text{CS,top}}}^{\texttt{z_cs_coil_upper}} + 0.1 \\ + \frac{1}{2}\left(\left(\underbrace{Z_{\text{TF,inside}}}_{\texttt{z_tf_inside_half}}-Z_{\text{CS,top}}\right)+\underbrace{dR_{\text{TF,inboard}}}_{\texttt{dr_tf_inboard}}+0.1\right)

Above the TF coils (one group only) | place_pf_above_tf()

  • i_pf_location(j) = 2;

    R = R_0 + \texttt{rpf2} \times \delta \times a

    Due to the nautre of the TF coils not being top-down symmetric for single null cases the positioning slightly differs if the coil is above or below the midplane.

    For above the midplane:

    Z = Z_{\text{TF,top}} + 0.86

    For below the midplane:

    Z = - \left(Z_{\text{TF,top}} - \overbrace{dZ_{\text{TF,upper-lower-midplane}}}^{\texttt{dz_tf_upper_lower_midplane}} + 0.86 \right)

Outside the TF coils | place_pf_outside_tf()

  • i_pf_location(j) = 3;

    The PF coils can either be stacked vertically outside the TF (ideal for a picture frame coil) or follow the TF coil curve (D-shaped):

    If the chosen value for i_tf_shape is that of a picture frame or i_r_pf_outside_tf_placement == 1 then:

    R = \overbrace{R_{\text{PF, outside-TF}}}^{\texttt{r_pf_outside_tf_midplane}}

    Else, the coils follow a D-shape curve

    R = \sqrt{\left(\overbrace{R_{\text{PF, outside-TF}}}^{\texttt{r_pf_outside_tf_midplane}}\right)^2 - Z^2}
    Z = \pm \ a \times \texttt{zref}

General placement | place_pf_generally()

  • i_pf_location(j) = 4;

    The PF coils are placed generally in units of minor radius (a) relative to the mid-plane and plasma major radius (R_0);

    R = \pm \ a \times \texttt{rref[]} + R_0
    Z = \pm \ a \times \texttt{zref[]}

Coil currents

The peak current per turn, c_pf_coil_turn_peak_input(i), and the winding pack peak current density j_pf_coil_wp_peak(i) in each PF coil i are inputs. The PF coil currents vary as a function of time during the tokamak operation as indicated in Figure 2. They contribute part of the flux swing necessary to maintain the plasma current.

Current waveform for Plasma, PF coil and Central Solenoid

Figure 2: Plot showing schematically the current waveforms for the plasma, a typical PF coil, and the central solenoid. Note that the currents in some of the PF coils may be the opposite sign to that shown, and the central solenoid current may remain positive during the Ip ramp-up period, although it will pass through zero during the burn phase.

Materials

The PF coils can be either resistive or superconducting. This is determined from the value of i_pf_conductor. If i_pf_conductor = 0, the PF coils and the central solenoid are assumed to be superconducting. If i_pf_conductor = 1, they are assumed to be resistive, with their resistivity given by the value of variable rho_pf_coil.

If i_pf_conductor = 0, switch i_pf_superconductor specifies which superconducting material is to be used for the PF coils. The values of i_pf_superconductor are used in the same way as switch isumattf is for the TF coils.

The fraction of copper present in the superconducting filaments if given by the value of variable fcupfsu.

If the PF coils are superconducting, a steel case is assumed to surround the current-carrying winding pack to take the hoop stress. Its cross-sectional area is determined by the J \times B hoop force on the coil divided by the allowable hoop stress, given by input parameter sigpfcalw. The input parameters sigpfcf provides a scale factor (default is 0.666) to adjust the hoop force if required, to indicate what proportion of the force is supported by the case.