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In physical theories, a 'test particle' is an idealised model of a small object some of whose physical properties (usually mass and size) are assumed to be negligible. The concept of a test particle simplifies some problems, and often provides a good approximation for physical phenomena in a specified domain of applicability.
In computer simulations, a 'test particle' is a particle whose movement according to potentials and the particles respective charge is traced (also called traced particles) but which does not otherwise interact with the system as other types of simulation particles usually would. The test particle method can be almost synonymous with a Monte Carlo method, though as a term it does not necessary involve any randomness, for example with respect to its initial location or velocity.

Contents

Classical Gravity

Test particles in general relativity

Test particles in plasma physics or electrodynamics

See also

References

Classical Gravity

The easiest case for the application of a test particle arises in Newtonian gravity. The general expression for the gravitational force between two masses $m\_1$ and $m\_2$ is:
:
where $r\_1$ and $r\_2$ represent the position of each particle in space. In the general solution for this equation, both masses rotate around their center of mass, in this specific case:
: Classical Mechanics, 2nd Ed., Herbert Goldstein, , , Addison-Wesley, ,

In the case where one of the masses is much larger than the other ($m\_1>>m\_2$), one can assume than the smaller mass moves as a test particle in a gravitational field generated by the larger mass, which remains immobile. By defining the gravitational field as

with $r$ as the distance between the two objects, the equation for the motion of the smaller mass reduces to

and thus only contains one variable, for which the solution can be calculated more easily. This approach gives very good approximations for many practical problems, e.g. the orbits of satellites, whose mass is relatively small compared to that of the earth.

Test particles in general relativity

In metric theories of gravitation, particularly general relativity, a test particle is an idealized model of a small object whose mass is so small that it does not appreciably disturb the ambient gravitational field.
According to the Einstein field equation, the gravitational field is locally coupled not only to the distribution of non-gravitational mass-energy, but also to the distribution of momentum and stress (e.g. pressure, viscous stresses in a perfect fluid).
In the case of test particles in a vacuum solution or electrovacuum solution, this turns out to imply that in addition to the tidal acceleration experienced by small clouds of test particles (spinning or not), ''spinning'' test particles may experience additional accelerations due to spin-spin forces. The Motion of Point Particles in Curved Spacetime Poisson, Eric

Test particles in plasma physics or electrodynamics

In simulations with electromagnetic fields the most important characteristics of a 'test particle' is its electric charge and its mass. In such simulations the particles are moved with the Lorentz force
$F\; =\; q\; (mathbf\{E\}\; +\; mathbf\{v\}\; imes\; mathbf\{B\})$,
where q is the particle's electric charge, 'v' its velocity and 'E' and 'B' the electric and magnetic fields, respectively.

See also

★ Papapetrou-Dixon equations

★ Magnetogravitic tensor and the Bel decomposition of the Riemann tensor

References