Researchers from the Complutense University of Madrid (UCM, Spain) have mathematically shown that particles charged in a magnetic field can escape into infinity without ever stopping. One of the conditions is that the field is generated by current loops situated on the same plane.
At the moment this is a theoretical mathematical study, but two researchers from UCM have recently proved that, in certain conditions, magnetic fields can send particles to infinity, according to the study published in the journal Quarterly of Applied Mathematics.
"If a particle 'escapes' to infinity it means two things: that it will never stop, and "something else," Antonio Diaz-Cano, one of the authors, explained. Regarding the first, the particle can never stop, but it can be trapped, doing circles forever around a point, never leaving an enclosed space.
However, the "something else" goes beyond the established limits. "If we imagine a spherical surface with a large radius, the particle will cross the surface going away from it, however big the radius may be" the researcher declares.
Scientists have confirmed through equations that some particles can escape infinity. One condition is that the charges move below the activity of a magnetic field created by current loops on the same plane. Other requirements should also be met: the particle should be on some point on this plane, with its initial speed being parallel to it and far away enough from the loops.
"We are not saying that these are the only conditions to escape infinity, there could be others, but in this case, we have confirmed that the phenomenon occurs," Diaz-Cano states. "We would have liked to have been able to try something more general, but the equations are a lot more complex."
In any case, the researchers recognise that the ideal conditions for this study are "with a magnetic field and nothing else." Reality always has other variables to be considered, such as friction and there is a distant possibility of going towards infinity.
Nonetheless, the movement of particles in magnetic fields is a "very significant" problem in fields such as applied and plasma physics. For example, one of the challenges that the scientists that study nuclear energy face is the confinement of particles to magnetic fields.
Accelerators such as Large Hadron Collider (LHC) of the European Organisation for Nuclear Research (CERN) also used magnetic fields to accelerate particles. In these conditions they do not escape to infinity, but they remain doing circles until they acquire the speed that the experiments need.
- A. Dνaz-Cano and F. Gonzαlez-Gascσn. Escape to infinity in the presence of magnetic fields. Quart. Appl. Math., August 26, 2011; 70 (2012), 45-51
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