European Space Agency

Royal Belgian Institute for Aeronomy

ud330 - evaluate the third invariant

subroutine  ud330(phi, star, ifail)

Parameters:

• phi [real8,out] :: Third invariant

• star [real8,out] :: Roederer’s parameter L*

• ifail [integer4,out] :: error flag (see Diagnostics)

Description

The subroutine ud330() computes the third invariant of the magnetic drift shell stored in the common block uc110, uc120 and uc130. The third invariant is evaluated by the integration of the magnetic flux over a spherical polar cap. Note that the subroutine needs the foot prints of the magnetic field lines contained in the drift shell. To this effect, the argument falt has to be set to a positive value when the subroutine ud310() is called to build the drift shell. The integration steps are controlled by the arguments epsomeg and dltlat of the common block uc192.

Roederer’s shell parameter L* is deduced directly from the value of the third invariant and of the moment M of the magnetic dipole. The value of M depends on the argument kmflg of the common block uc190.

References

• Roederer, J.G., Dynamics of geomagnetically trapped radiation, Springer-Verlag (1970)

Diagnostics

None

Common Blocks

• uc110 - magnetic drift shell

• uc140 - magnetic field

• uc160 - general constants

• uc190 - control parameters, set 1

Dependencies

Called by

None

Calls

• ud331 - evaluate the magnetic flux through a spherical cap

See also

• ul240 - evaluate the Hilton’s function

• ud310 - trace a magnetic drift shell

Reported Bugs

None

Examples

• Ex #3. Evaluation of the third invariant

• T.04 - Why are Roederer’s L* and McIlwain’s L parameters different ?

---

UNILIB/tags/v3.02