Start field namelist

This namelist controls whether a start field from a previous solution should be used, or a specific field should be initialized.

Reading an input file of start fields

• l_start_file (default l_start_file=.false.) is a logical that controls whether the code should to read a file named start_file or not.

• start_file (default start_file="no_start_file") is a character string. This is the name of the restart file.

• inform (default inform=-1) is an integer that can be used to specify the format of start_file. This ensures possible backward compatibility with previous versions of the code. You shouldn’t change this value except to read very old checkpoint_end.TAG files generated by older versions of MagIC.

  inform=0	Oldest format used by U. Christensen
  inform=1	Newer format used by U. Christensen
  inform=2	Inner core introduced by J. Wicht
  inform=-1	Default format

• scale_s (default scale_s=1.0) is a real. It can be possibly used to multiply the input entropy field from start_file by a constant factor scale_s.

• scale_xi (default scale_xi=1.0) is a real. It can be possibly used to multiply the input chemical composition field from start_file by a constant factor scale_xi.

• scale_v (default scale_v=1.0) is a real. It can be possibly used to multiply the input velocity field from start_file by a constant factor scale_v.

• scale_b (default scale_b=1.0) is a real. It can be possibly used to multiply the input magnetic field from start_file by a constant factor scale_b.

• tipdipole (default tipdipole=0.0) is a real that can be used to add non-axisymmetric disturbances to a start solution if non-axisymmetric parts have been lost due to mapping to a different symmetry. A \((\ell=1,m=1)\) entropy term is added with:

  \[s_{10}(r) = \hbox{tipdipole}\,\sin [\pi (r-r_i) ]\]

  If a magnetic field without an \(m=1\) term is mapped into a field that permits this term, the code adds the respective poloidal field using the \((\ell=1,m=0)\) poloidal magnetic field and scaling it with tipdipole.

• l_reset_t (default l_reset_t=.false.) is a logical that can be set to .true. in case one wants to reset the time of start file to zero.

Defining the starting conditions

Initialisation of entropy

The heat equation with possible heat sources and sinks given by epsc0 is solved for the spherically-symmetric term \((\ell=0,m=0)\) to get its radial dependence. In addition to this initial state, two other laterally varying terms can be initialized. Their radial dependence are assumed to follow:

\[s(r) = 1-2\,x^2+3\,x^4-x^6,\]

where

\[x = 2\,r-r_o-r_i\, .\]

The initial perturbation is thus set to zero at both boundaries \(r_i\) and \(r_o\), and reaches its maximum amplitude of amp_s1 or amp_s2 at the mid-shell radius \(r_i+1/2\).

• init_s1 (default init_s1=0) is an integer that controls the initial entropy. The following values are possible:

  • init_s1=0: nothing is initialized

  • init_s1<100: a random-noise of amplitude amp_s1 is initialised. The subroutine initS in init_fields.f90 gives the detail of this implementation.

  • init_s1>100: initialisation of mode with the spherical harmonic order \(m\) given by the last two (or three) digits of init_s1 and the spherical harmonic degree \(\ell\) given by the first two (or three) digits. Here are two examples:

    init_s1  = 0707,
    amp_s1   = 0.05,
    

    will introduce a perturbation on the mode \((\ell=7,m=7)\) with an amplitude of 0.05.

    init_s1  = 121121,
    amp_s1   = 0.01,
    

    will introduce a perturbation on the mode \((\ell=121,m=121)\) with an amplitude of 0.01.

• amp_s1 (default amp_s1=0.0) is a real used to contol the amplitude of the perturbation defined by init_s1.

• init_s2 (default init_s2=0) is an integer that controls a second spherical harmonic degee. It follows the same specifications as init_s1.

• amp_s2 (default amp_s2=0.0) is a real used to contol the amplitude of the perturbation defined by init_s2.

Initialisation of chemical composition

The chemical composition equation with possible volumetric sources and sinks given by epscxi0 is solved for the spherically-symmetric term \((\ell=0,m=0)\) to get its radial dependence. In addition to this initial state, two other laterally varying terms can be initialized. Their radial dependence are assumed to follow:

\[\xi(r) = 1-2\,x^2+3\,x^4-x^6,\]

where

\[x = 2\,r-r_o-r_i\, .\]

The initial perturbation is thus set to zero at both boundaries \(r_i\) and \(r_o\), and reaches its maximum amplitude of amp_xi1 or amp_xi2 at the mid-shell radius \(r_i+1/2\).

• init_xi1 (default init_xi1=0) is an integer that controls the initial chemical composition. It follows the same specifications as init_s1.

• amp_xi1 (default amp_xi1=0.0) is a real used to contol the amplitude of the perturbation defined by init_xi1.

• init_xi2 (default init_xi2=0) is an integer that controls a second spherical harmonic degee. It follows the same specifications as init_s1.

• amp_xi2 (default amp_xi2=0.0) is a real used to contol the amplitude of the perturbation defined by init_xi2.

Initialisation of phase field

• init_phi (default init_phi=0) is a integer used to specify the initial phase field. If init_phi /= 0 a tanh profile centered around the melting temperature is used.

Initialisation of magnetic field

• init_b1 (default init_b1=0) is an integer that controls the initial magnetic field. The following values are possible:

  • init_b1<0: random noise initialization of all \((\ell,m)\) modes, except for \((\ell=0,m=0)\). The subroutine initB in the file init_fields.f90 contains the details of the implementation.

  • init_b1=0: nothing is initialized

  • init_b1=1: diffusive toroidal field initialized. Mode determined by imagcon.

  • init_b1=2: \((\ell=1,m=0)\) toroidal field with a maximum field strength of amp_b1. The radial dependence is defined, such that the field vanishes at both the inner and outer boundaries. In case of an insulating inner core: \(h(r)\approx r\,\sin[\phi(r-r_o)]\). In case of a conducting inner core: \(h(r)\approx r\,\sin[\pi(r/r_o)]\).

  • init_b1=3: \((\ell=1,m=0)\) poloidal field whose field strength is amp_b1 at \(r=r_i\). The radial dependence is chosen such that the current density \(j\) is independent of \(r\):, i.e. \(\partial j /\partial r = 0\). \((\ell=2,m=0)\) toroidal field with maximum strength amp_b1.

  • init_b1=4: \((\ell=1,m=0)\) poloidal field as if the core were an insulator (potential field). Field strength at \(r=r_i\) is again given by amp_b1.

  • init_b1=5: \((\ell=1,m=0)\) poloidal field with field strength amp_b1 at \(r = r_i\). The radial dependence is again defined by \(\partial j/\partial r= 0\).

  • init_b1=6: \((\ell=1,m=0)\) poloidal field independend of \(r\).

  • init_b1=7: \((\ell=1,m=0)\) poloidal field which fulfills symmetry condition in inner core: \(g(r)\approx \left(\frac{r}{r_i}\right)^2\left[1-\frac{3}{5}\left(\frac{r}{r_o}\right)^2\right]\). The field strength is given by amp_b1 at \(r = r_o\).

  • init_b1=8: same poloidal field as for init_b1=7. The toroidal field fulfills symmetry conditions in inner core and has a field strength of amp_b1 at \(r = r_i\): \(h(r)\approx \left(\frac{r}{r_i}\right)^3\left[1-\left(\frac{r}{r_o}\right)^2\right]\).

  • init_b1=9: \((\ell=2,m=0)\) poloidal field, which is a potential field at the outer boundary.

  • init_b1=10: equatorial dipole only.

  • init_b1=11: axial and equatorial dipoles.

  • init_b1=21: toroidal field created by inner core rotation, equatorially symmetric \((\ell=1,m=0)\): \(h(r)= \hbox{ampb1}\, \left(\frac{r_i}{r}\right)^6\). The field strength is given by amp_b1 at \(r=r_i\).

  • init_b1=22: toroidal field created by inner core rotation, equatorially antisymmetric \((\ell=2,m=0)\). Same radial function as for init_b1=21.

• amp_b1 (default amp_b1=0.0) is a real used to contol the amplitude of the function defined by init_b1.

• imagcon (default imagcon=0) is an integer, which determines the imposed magnetic field for magnetoconvection. The magnetic field is imposed at boundaries.

  • imagcon=0: no magneto-convection

  • imagcon<0: axial poloidal dipole imposed at ICB with a maximum magnetic field strength amp_b1.

  • imagcon=10: \((\ell=2,m=0)\) toroidal field imposed at ICB and CMB with a maximum amplitude amp_b1 at both boundaries.

  • imagcon=11: same as imagcon=10 but the maximum amplitude is now amp_b1 at the ICB and -amp_b1 at the CMB.

  • imagcon=12: \((\ell=1,m=0)\) toroidal field with a maximum amplitude of amp_b1 at the ICB and the CMB.

• tmagcon (tmagcon=0.0) is a real.

Initialisation of velocity field

• init_v1 (default init_v1=0) is an integer that controls the initial velocity. The following values are possible:

  • init_v1=0: nothing is initialized

  • init_v1=1: a differential rotation profile of the form

    \[\begin{split}\Omega = \Omega_{ma}+0.5\Omega_{ic} \quad\hbox{for}\quad s\leq r_i \\ \Omega = \Omega_{ma} \quad\hbox{for}\quad s> r_i\end{split}\]

    where \(s=r\sin\theta\) is the cylindrical radius. This profile only makes sense when one studies spherical Couette flows.

  • init_v1=2: a differential rotation profile of the form \(\Omega= \frac{\hbox{ampv1}}{\sqrt{1+s^4}}\) is introduced.

  • init_v1>2: a random-noise of amplitude amp_v1 is initialised. The subroutine initV in init_fields.f90 gives the detail of this implementation.

• amp_v1 (default amp_v1=0.0) is a real used to contol the amplitude of the function defined by init_v1.