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Contents

Geometry

Coordinates

GYRO uses a right-handed, field-aligned coordinate system (r,\theta,\alpha)\,\! and the Clebsch field representation

\mathbf{B} = \nabla\alpha \times\nabla\psi(r)

where \psi\,\! is the poloidal flux divided by 2\pi\,\! and

\alpha = \varphi + \nu(r,\theta)

is the Clebsch angle. Note also that \varphi\,\! is the usual toroidal angle.

Equilibria

GYRO can be run using either circular equilibrium or Miller shaped equilibrium:

Circular equilibrium

  • Select RADIAL_PROFILE_METHOD=1 (local simulations only).
  • In this case the flux-surface is nothing but a circle:
R(r,\theta) = R_0 + r \cos\theta\,\!
Z(r,\theta) = r \sin \theta\,\!
\nu(r,\theta) = -q(r)\theta\,\!

Miller shaped equilibrium

R(r,\theta) = R_0(r) + r \cos\left( \theta + \arcsin\left[\delta(r)\right] \sin\theta\right)\,\!
Z(r,\theta) = \kappa(r) r \sin\theta\,\!
\nu(r,\theta)\,\! must be computed numerically.

Table of geometry parameters

Symbol INPUT Parameter Circular Miller
R_0(r)/a\,\! ASPECT_RATIO x x
r/a\,\! RADIUS x x
q\,\! SAFETY_FACTOR x x
s\,\! SHEAR x x
\beta_*\,\! BETAE_UNIT ALPHA_MHD x x
\partial R_0/\partial r \,\! SHIFT x
\kappa\,\! KAPPA x
s_\kappa\,\! S_KAPPA x
\delta_0\,\! DELTA0 x
s_{\delta_0}\,\! S_DELTA0 x
\delta_1\,\! DELTA1 x
s_{\delta_1}\,\! S_DELTA1 x


To understand the Miller local equilibrium model, geometry and normalization conventions consult the Technical Manual, which can be obtained throught the GYRO CVS.

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