The function returns the energy of a positively charged isotope of hydrogen when it escapes a particle accelerator, and the number of times the isotope enters two vacuum chambers, after a voltage is applied to it.
The input argument (must be a scalar) is the voltage applied to a cyclotron (see attached figure), which is a device that accelerates subatomic particles (positively charged isotopes of hydrogen, called “deuterons”) which spiral outward in a clockwise direction. The cyclotron rapidly alternates the sign of the voltage difference V in units of volts between two “D”-shaped vacuum chambers (blue outlines in the figure), which are placed within a strong uniform magnetic field (not shown but perpendicular to the screen). The deuteron is accelerated only as it is leaving one “D” and entering the other. While the deuteron is inside a given “D”, it moves at a constant speed, and the magnetic field causes it to move on a semicircle. Each deuteron moves as follows (check the numbers in the figure): (1) It originates from a source (red dot) located at a distance 𝑠𝑠0 to the left of the center of the cyclotron, is accelerated vertically into the upper “D” and then moves on a semi-circle of radius r1. (2) It leaves the upper “D” and is accelerated vertically downward into the lower “D” where it moves with a larger radius r2. (3) It leaves the lower “D” and is accelerated vertically into the upper “D”, etc, moving with ever increasing radii until (N) it is accelerated for the final time as it leaves the upper “D” and enters the lower “D”, follows a semicircle, and emerges from the cyclotron at the left. The deuteron escapes through a window at the left that is placed so the particle cannot leave until it is more than 0.500 meters to the left of the center of the cyclotron. The gap between the “D”s is exaggerated in the figure, has no effect, and can be assumed to be of zero width. The function returns the energy E of the deuteron when it escapes in units of million electron volts (MeV), and the number N of times the deuteron enters the “D”s. Notice that the centres of the semicircles ≠ the center of the cyclotron.