# Plasma shaping

Magnetically confined fusion plasmas such as those generated in tokamaks and stellarators are characterized by a typical shape. Plasma shaping is the study of the plasma shape in such devices, and is particularly important for next step fusion devices such as ITER. This shape is conditioning partly the performance of the plasma. Tokamaks, in particular, are axisymmetric devices, and therefore one can completely define the shape of the plasma by its cross-section.

Early fusion reactor designs tended to have circular cross-sections simply because they were easy to design and understand. Generally, fusion machines using a toriodal layout, like the tokamak and most stellarators, arrange their magnetic fields so the ions and electrons in the plasma travel around the torus at high velocities. However, as the circumference of a path on the outside of the plasma area is longer than one on the inside, this caused several effects that disrupted the stability of the plasma.

During the 1960s a number of different methods were used to try to address these problems. Generally they used a combination of several magnetic fields to cause the net magnetic field inside the device to be twisted into a helix. Ions and electrons following these lines found themselves moving to the inside and then outside of the plasma, mixing it and suppressing some of the most obvious instabilities. In the 1980s, further research along these lines demonstrated that further advances were possible by making the lines not just helical, but non-symmetric as well. This led to a series of experiments using C and D-shaped plasma volumes.

## Cross-section

In the simple case of a plasma with up-down symmetry, the plasma cross-section is defined using a combination of four parameters:

• the plasma elongation, $\kappa={b \over a}$, where $a$ is the plasma minor radius, and $b$ is the height of the plasma measured from the equatorial plane,
• the plasma triangularity, defined as the horizontal distance between the plasma major radius $R$ and the X point,
• the angle between the horizontal and the plasma last closed flux surface (LCFS) at the low field side,
• the angle between the horizontal and the plasma last closed flux surface (LCFS) at the high field side.