# Toroidal magnetic field measurements

The toroidal magnetic field $$B_T$$ is measured by a small coil (called the $$B_T$$ coil) fixed to the tokamak upper outboard side, its axis pointing along the torodial direction. The general principle of magnetic coil measurements is described here. The $$B_T$$ coil is one of the basic GOLEM diagnostics.

# Coil description

The $$B_T$$ coil is made of 255 turns, each having a diameter of $$10 \, \mathrm{mm}$$. Its effective area is therefore $$0.02 \, \mathrm{m}^2$$. Its exact coordinates in the $$(R,Z)$$ plane are not known but this isn’t an issue; see below. The coil voltage is collected by the DAS1 data acquisition system.

## Coil effective area for area-averaged $$B_T$$ measurements

There is a large loop encircling the tokamak chamber in the poloidal direction; its radius is $$0.145 \, \mathrm{m}$$ and its area is $$0.066 \, \mathrm{m}^2$$. Even though it is not currently part of the tokamak diagnostic system, it can be used for measurements of $$B_T$$ averaged over the entire loop area. It was measured that when the $$B_T$$ coil signal is averaged over this area (considering that $$B_T \sim 1/R$$), its sensitivity is $$5.98 \div 6.06$$ times lower than the large loop sensitivity. This implies that the $$B_T$$ coil effective area is $$0.066 \, \mathrm{m}^2 / 6 = 0.011 \, \mathrm{m}^2$$ when it’s used for area-averaged $$B_T$$ measurements.

# $$B_T$$ measurement

Cannonically the toroidal field $$B_T$$ is always given at the chamber centre. This is because it falls with the major radius as $$B_T \sim 1/R$$, and so a fixed measurement location is required to compare between various tokamaks and discharges. Unfortunately the $$B_T$$ coil is not located at $$R=R_0$$; rather it is further outside. However, since the chamber doesn’t move anywhere and neither does the coil, the ratio $$B_{T0}/B_{T,coil}$$ is fixed. Many years ago a calibration experiment was conducted where a measuring coil was inserted into the centre of the tokamak chamber. By comparing its signal to the $$B_T$$ coil signal, the following calibration relation was derived:

$B_{T0}(t) = 70.42 \, \mathrm{T/Vs} \int_0^t V_{coil}(t') \mathrm{d}t'$

Here $$V_{coil}$$ is the voltage induced on the $$B_T$$ coil. The constant $$70.42 \, \mathrm{T/Vs}$$ [source] is several calibration constants combined into one. It includes both the calibration “induced voltage $$V_{coil} \rightarrow$$ magnetic field $$B_{T,coil}$$” (featuring the number of coil turns and the coil effective area) and the calibration “$$B_{T,coil} \rightarrow B_{T0}$$”.

• find which DAS the $$B_T$$ coil is plugged into