Table of contents

1. Overview of Planetocosmics and Planetocosmics-J
2. Planetocosmics-J in the SPENVIS environment
3. Source
4. Planetary settings
   1. Magnetic field
   2. Surface conditions
5. Geometry
6. Analysis parameters
   1. Particle fluxes
   2. Energy deposition
   3. Particle rigidity
7. Material definition
8. Stopping conditions
9. Results
10. References

Overview of Planetocosmics and Planetocosmics-J

The original Planetocosmics application developed by Desorgher allows the definition of a planetary magnetic field, atmosphere and soil. The version currently implemented in SPENVIS is applicable for Mercury, Earth and Mars. Planetocosmics uses the Geant4 radiation simulation toolkit to model the hadronic and electromagnetic interactions of cosmic rays and solar particles with the planetary environment, thereby providing an extremely comprehensive treatment of the particle interaction processes.

Planetocosmics-J,^[1,2] developed by QinetiQ, is an update of version 2.0 of the Planetocosmics code which can treat the particle interactions for the Galilean moons Io, Europa, Ganymede and Callisto. The tool is considered applicable to the following two study categories:

1. Simulation of particle propagation near Galilean moons

The primary use-case for Planetocosmics-J is intended to be the direct simulation of the Jovian trapped radiation environment at the Galilean moons. For this, the model has been modified to include the internal/induced magnetic fields of the Galilean moons, as well as the large scale magnetic field from Jupiter and its potential fluctuations. This helps provide better predictions of the trapped radiation levels at the surface of the moons, including the secondary radiation backscatter (such as bremsstrahlung from electrons or neutrons from incident protons and other ions) from the surface of the moon. In addition, the shielding effects of Europa, due to the depletion of trapped particles from the Jovian magnetosphere as the belts sweep-by the moon, can also be studied due to the treatment of particle mirroring and eastward drift effects for particles in the Jovian magnetosphere.

2. Calculation of cutoff rigidities for Ganymede

Planetocosmics-J may be useful for determining cutoff rigidities in the combined moon internal and Jovian magnetic field at Ganymede, and therefore the flux of particles from the Jovian magnetosphere reaching a particular location within the Ganymede magnetic field.

The user should note that these simulations can be highly time-consuming. Thus, since the CPU time available on SPENVIS for a single user is limited, the calculations are stopped if the program duration time exceeds a limit. This can be often the case for calculations on maps or orbit trajectories. Therefore, users are welcome to utilize SPENVIS to produce and download the macro file but is recommended that they download the stand-alone version of Planetocosmics-J to make a run.

Note that like Planetocosmics, Planetocosmics-J makes use of the Geant4 toolkit ^[12]. The complete Planetocosmics-J user manual is available online as a PDF-document.

Planetocosmics-J in the SPENVIS environment

The SPENVIS interface to Planetocosmics-J simplifies the process of defining run parameters via a number of input pages (see below) that a user can access from a table on the main page of the model. In addition, some information on the status and a short summary of the user input is also displayed.

Users can go to any particular input page and enter their settings. After they are done, they can hit the button and return to the main model page. Once they are satisfied with all their input they can use the button to generate the macro file. Pressing the button will start the calculation and bring up the results page.

Since the model uses a Monte-Carlo simulation-based code, execution times can be very long, certainly for cut-off calculations. The execution is limited to five minutes of CPU-time on the simulation machine. If the Planetocosmics-J run exceeds this limit, the simulation will be terminated and intermediate results returned to the user.

Source particles

Users can specify the incident particle, its energy spectrum and angular distribution using a template very similar to the generic source particles template. Since Planetocosmics-J addresses the propagation of Jovian trapped particles, the usual condition is to start the particles at a point or plane in front of or behind the Galilean moon, so that the combined effects of rotation of the Jovian plasmasphere, the rotation of the moon and v x B drift sweeps the particles towards or indeed away from the moon, depending upon charge and energy.

Planetary settings

A user can provide input, when applicable, defining the magnetic field and surface conditions of the a particular moon. Whilst there is some evidence of an atmosphere for the larger moons, this is sufficiently tenuous to have insignificant impact on particle propagation.

Magnetic field

There are several options for treating Jupiter’s internal and external magnetic field, as defined in the table below.

Jovian internal field models	Jovian external field models
P11: Pioneer 11 model from Davis et al. (1975)	Khurana (1997) model based on data from Pioneer 10[7]
O4: Model of Acuna and Ness (1976)[3,4]	Khurana (1997) model based on data from Voyager 1[7]
O6: Model of Connerney (1993)	Khurana (1997) model based on data from Voyager 2[7]
ULYSSES: Ulysses inner field model from Dougherty et al. (1996)	Khurana’s model for magnetic field of a tilted and warped shielded magnetosphere using general deformation technique
VIP4: Connerney et al. model (1998)

Intrinsic field models are available for Io and Ganymede. For Io, this model comes from Kivelson et al., i.e. it is a simple dipole of strength of 540 nT, centred at the geometric centre of the moon and spin axis aligned^[8]. Ganymede’s intrinsic field is a more complex spherical harmonic expansion of the field based on Galileo data and comes from Kivelson, Khurana and Volwerk^[9]. The coefficients correspond to a dipole of magnitude 719±2 nT, tilted at 176°±1° to the spin axis, with the southern hemisphere pole rotated 24°±1° from the Jupiter facing meridian.

Within PLANETOCOSMICS-J there is an induced field model based broadly on that of Zimmer et al.^[10], assuming a dipolar induced field at position r from the moon’s centre and time t given by [10]:

where B_sec is in units of nanotesla and:

• A and φ: amplitude and phase coefficients associated with the response of the subsurface ocean to the Jovian (primary) magnetic field (A is unitless and φ has units of degrees);
• ω: rotation rate of the Jovian field with respect to the moon;
• B_J(t’): local Jovian field at moon at time t’ [nT];
• r_m: radius of moon [m];
• r: distance from the moon, i.e. |r| [m];
• r: unit vector for position vector r, i.e. radial unit vector from moon;
• e₀: unit vector for direction of local Jovian field at moon, i.e.
  

Surface environment

All the moons share the same options for the definition of the soil: default composition, soil not taken into account, or 1, 2 or 3 layers. When the surface ("soil") is defined in terms of soil layers (up to three layers), a user can specify the composition (material) and the thickness of the layer(s). A link to the material definition tool is also available via the edit materials link.

The default for the surfaces of Europa, Ganymede and Callisto is H₂O (assumed to be ice) with a density of 1.0 g cm^-3 and thickness of 10 m. Whilst there is evidence from Galileo of inclusions within the ice, the contributions and variability of the included material at the first millimetre is still not that well defined for the surfaces of the moons, let alone at tens of centimetres into the surface. For Io, volcanic basalt surface is assumed to comprise the following elements, providing a material density of 2.2 g cm^-3 to a thickness of 10 m:

Material	S	Na	Mg	Fe	O	H
Abundance [%]	62.5	2.2	1.1	5.2	27.7	1.3

Geometry

Unlike Planetocosmics, Planetocosmics-J only supports spherical geometries and not planar ones. The coordinate system is PhiO, i.e. GPhiO for Ganymede, EPhiO for Europa, etc. In the PhiO coordinate system, the positive X axis points in the flow direction, the Y axis points from the moon centre to Jupiter’s centre and Z is along the moon’s rotational (i.e. spin rather than orbital) axis. For coordinate transformations from Jupiter to the moon, since the spin axes of both bodies are nearly parallel, it has been assumed for Planetocosmics-J that the System III Z axis for Jupiter is parallel to the PhiO Z axis for the Galilean moons.

Analysis parameters

There are three possible types of analysis available in the SPENVIS implementation of Planetocosmics-J: particle fluxes, energy deposition, and rigidity calculation. The first two cases are identical to the standard Planetocosmics analysis.

Particle fluxes

Planetocosmics-J can register the flux of primary and secondary particles as a function of kinetic energy. The user can provide the number of energy bins dividing the energy axis and the binning mode. The energy range can be specified by providing a minimum and a maximum energy value. In addition, one can choose one or more secondary particle types to be considered in the analysis. Finally, a user can define up to 5 detectors by providing the detector's altitude in m or km. Note that these detectors indicate the altitudes where fluxes of shower particles will be registered during the Planetocosmics-J simulation.

Energy deposition

Planetocosmics-J can calculate the energy deposited by incident particles in the surface as a function of soil thickness and depth. The user can provide the number of bins dividing the depth/thickness axis for the surface.

Particle rigidity

Planetocosmics-J can calculate the particle cut off rigidities for particles approaching a grid of points (defined in PhiO longitude, latitude and altitude) with a particular direction (defined in terms of azimuth and zenith). The user can provide the number of bins dividing the rigidity scale.

Material definition

Users can employ the "material definition tool" to either specify their own material or make use of the predefined lists.

Stopping conditions and additional physics

Planetocosmics-J includes, by default, treatment of vxB forces for charged particles. The slower orbital period of Europa and Ganymede with respect to the combined motion of the Jovian plasmasphere rotation, and the E/W drift period of the particles, result in an additional complexity to the radiation environment in very close proximity to the moons. Since the field lines of Jupiter’s magnetic field sweep from the trailing hemisphere to the leading hemisphere, the plasma overtakes the moon, resulting in particle deposition in the trailing hemisphere as they spiral around the field lines between the mirror points. The particle populations along those field lines will therefore be depleted and the ram-direction ("shadow") of the moon experiences much lower doses. For sufficiently high-energy electrons, however, the grad-B and curvature drifts which move the particles in a westward direction are faster than the relative rotations of the Jovian magnetic field and moon. For Europa, therefore, electrons less than ~25 MeV approach from the trailing hemisphere (-X EPhiO) whilst electrons greater than this energy approach from the leading hemisphere (+X EPhiO).

Additional parameters associated with this model allow the user to introduce a degree of instability in the field line, so that the new position of the guiding centre follows a radial Gaussian probability distribution with the value for σ defined by the user.

In order to limit the computing time during a Geant4 simulation, secondary electrons, protons and gamma's are tracked only if their range in the material where they are produced is higher than the cut in range parameter.

Results

Planetocosmics-J produces the files listed in the table below. The macro file spenvis_pcj.g4mac contains the Geant4 macro file. The log file spenvis_pcj.g4log records the output from Planetocosmics-J to stdout and stderr. The output file spenvis_pcj.txt contains tabulated results according to the selected analysis scenario (particle fluxes or energy deposition).

Output files generated by Planetocosmics-J

File name	Description
spenvis_pcj.g4mac	Geant4 macro file
spenvis_pcj.g4log	Log file
spenvis_pcj.txt	Outputs for the various analysis types

To generate plots, select the plot type(s), options and graphics format when applicable, and click the button. The current page will be updated with the newly generated plot files.