How to define spacecraft equivalent circuit?

 

This page describes how the spacecraft equivalent is modelled in SPIS, and how the user inputs allow defining it.

 

Introduction

 

Spacecraft electrical behaviour can be modelled by an electric circuit collecting and emitting currents from and to the plasma. Some electric components of the equivalent circuit are just a way to mimic materials (e.g. a dielectric coating is equivalent to a capacitor, possibly with a resistor in parallel), while others are real physical devices (e.g. a potential supply between SC ground and a Langmuir probe, a resistor between SC and solar array grounds). Some components are also uniform over a subsystem of spacecraft (a coated area), while others are unique. Both notions most often coincide: uniform areas of coating equivalent to resistors and capacitors (we can call them continuous components), and a few real discrete devices (we can call them discrete components). The type and values of the continuous components can be derived from the material properties (and dynamically from particle flux for radiation induced conductivity), while the discrete components have to be defined by user through extra data not deriving from coating or any local data.

 

It was thus decided to have an automated derivation of the continuous components from coating data, while the discrete data have to be defined in an extra file. Of course another reason of that choice is that defining a huge number of local values for continuous components was not reasonable.

 

Continuous components

 

Continuous components are thus derived from the user-defined material properties (mostly local fields). Note also that they are affected by the switching on and off of conductivities (volume, induced in volume, and surface) through three global parameters. Their equivalent circuit is the following:

 

 

Discrete components

 

Discrete components are not plugged on top of coated surfaces, but between conductive parts of sub-systems, which may be considered as a sub-system ground. The notion of electric (super) node was defined to represent such local grounds (a piece of conductor indeed as the thick line on the figure above). So, an electric super node can be the ground of SC (predefined Id 0), a solar array ground, the box/ground of a system, the biased part of a device�

 

Electric (super) nodes must first be defined. This is done through the local field elecNodeId. The (super) node Id is mapped by the code on each elementary surface of the mesh from the definition by the user at group level. For each elementary mesh surface coated by a dielectric an extra elementary node and extra capacitors and resistors are automatically generated by the code (left hand side of the figure above), while no extra node or component is added if uncoated or coated by a conductive coating (right hand side of the figure above).

NB: node 0 is considered as spacecraft ground, with the only real consequence that it always exists (other nodes only exist if their Id appear somewhere on the spacecraft).

 

Discrete devices then have to be plugged between the electric (super) nodes. They are defined by the user in a file of a user-specified name (default name is "circuit.txt"). The syntax of the circuit file is described in the UI description page. It supports capacitors, resistors, active bias and inductances (since SPIS v4.0). An example of global circuit, including continuous and discrete components is given here:

 

 

Note that there is a special requirement if you want to link more than two super nodes by voltage generators. This is a rare situation, but it may be used to simply connect different nodes (0 bias). The network of voltage generators between the connected nodes can be re-arranged freely, provided correct voltages are computed. In the current status of the solver the rule is that it should be rearranged so that all nodes are connected to a common node (network in the shape of a star), with the node to all voltage generator bearing the smallest number.

There is of course another constraint for such a network of biases: no loop is allowed (whether the applied biases are consistent with such a loop or not).

 

 

Spacecraft Capacitance, Csat

 

Spacecraft capacitance is defined as the ratio of the total charge on an equipotential spacecraft to its potential: � Qsat = Csat Vsat.

It can be seen as "component" capacitor plugged between the spacecraft at plasma ground located at infinity. Electrodes are indeed the charges on top of spacecraft surfaces and in its sheaths.

This capacitance value depends on plasma conditions. In a code it can either be computed or user-defined. In SPIS it is defined as the global parameter CSat.

For a non conductive non equipotential spacecraft Csat may be plugged from plasma ground to different parts of the spacecraft. By default Csat is spread over all spacecraft local grounds in proportion to their respective areas Ai, as depicted in this circuit:

This is representative of a sheath uniform all over the spacecraft, resulting in local capacitance to be proportional to area.

 

In some cases the user may yet want to plug Csat to a specific part of the spacecraft. It is possible to plug it to spacecraft ground only:

by defining a negative Csat (its absolute value is used by the code, of course).

Be aware that the equations resulting from the circuit above are singular: nodes 1 and 2 have no capacitive or other coupling to any other node or ground. They are thus interpreted as having zero capacitive coupling, which means that the smallest collected charge results in an infinite potential (if circuit is integrated). In this case extra components should thus be added in general (user-defined capacitors between nodes, biases, etc.). This does not happen in the regular situation of a Csat spread over the whole spacecraft (CSat > 0).

 

 

Initialisations

 

At simulation start, potentials have to be initialised (and capacitor charges consistently). They may then remain unchanged or be modified if electric circuit integration is switched on (electricCircuitIntegrate parameter).

 

There are 2 different types of initialisations:

-         the initPot local field defines the potential on top of coatings

-         the definition of an active bias between two super nodes initialises (but permanently!) the potential between the nodes. Electric super nodes are first initialised to 0 potential. Then the rule is that V Node1 Node2 deltaV forces node2 potential to be node1 potential + deltaV.

For a coated surface the potential on top of the coating ("upper" capacitor electrode) is thus defined by initPot, while the potential on ground below ("lower" capacitor electrode) is defined the circuit definition (discrete device). For a conductive surface, the two initialisations may collide: if an active potential is imposed to a conductive node, the local values obtained from initPot are overridden by the potential imposed by the bias defined in the circuit file.

 

A richer panel of initialisation capabilities may be offered in future if needed (e.g. not-permanent non-zero initialisation of super node grounds), but it was not found very useful now.