Historical research guide · 0394 · 2020
Accurately predicting electron beam deflections in fringing fields of a solenoid
Christof Baumgärtel · Ray T. Smith · Simon Maher
In one minute
Christof Baumgärtel, Ray Smith and Simon Maher at the University of Liverpool built a deliberately plain experiment: an electron gun salvaged from an oscilloscope fires a beam past a current-carrying solenoid, and the deflected spot is read off a phosphor screen. Then they predicted that deflection three ways. Two are standard field theory — the textbook Maxwell-Lorentz calculation, and CPO, a commercial charged-particle package. The third drops fields altogether and uses Wilhelm Weber’s force, in which two charges act on each other directly along the line joining them, with corrections for their relative velocity and acceleration. Across three solenoids and every beam position, including the awkward fringe regions at the ends where the field bulges outward, the Weber calculation matched the measurements to 91.7 per cent on average, against 73.2 per cent for the commercial software and 67.4 per cent for the analytic field model. The authors are careful about scope: this is the slow-electron regime, and they present the two pictures as complements rather than rivals.
Connection
Chapter 10 asks what the potentials and the phase of a field actually are, and this is one of the few modern papers that puts a direct-action alternative to field theory on a bench and scores it against the standard calculation on real numbers. Chapter 3 reads inertia and gravity the same way — as an interaction with a medium rather than as fields treated as things in themselves — so a clean win for direct action in the fringe region is worth watching.
From the source
Averaged over three solenoids and every beam position, the direct-action Weber model predicted the measured deflections to 91.7 per cent accuracy, against 73.2 per cent for the commercial boundary-element package CPO and 67.4 per cent for the analytic Maxwell-Lorentz field model.Results and discussion, paragraph after Eq. 31; Tables 2 and 3
The experiment is a modified Hameg oscilloscope electron gun at 2000 volts, giving electrons about 2.65 times 10 to the 7th metres per second, fired 18.5 cm past solenoids of 25 mm, 255 mm and 500 mm length carrying 1.00 A, with the spot position read on a 10 mm graticule and each measurement repeated three times.Experimental setup; Table 1; Eq. 30
The gap is widest exactly where fringing is strongest: at half the solenoid length on the 500 mm solenoid the measured horizontal deflection was 25.2 mm, the Weber model gave 25.3 mm and the analytic field model 32.2 mm.Table 3, solenoid S3 at half the solenoid length
The Weber force acts along the line joining two charges, depends on their separation, relative velocity and relative acceleration, and reduces to the Coulomb force for charges at rest; the model computes the deflecting force directly, without constructing a magnetic field, a leakage flux or a vector potential.Mathematical model, Weber model, Eqs. 2 to 6; Conclusion, third paragraph
Two independent formulations of the winding — a helix that follows the pitch, and a summation over single loops — give the same force, and the longitudinal force along the beam comes out zero, agreeing with the Lorentz-force vector.Weber model, paragraph following Eq. 20
The result is claimed only for the low-velocity regime; the authors name the open problem, that direct action needs amendment as charges approach the speed of light, and cite the work attempting it.Conclusion, final paragraph, citing references 54 and 55
The way in
https://doi.org/10.1038/s41598-020-67596-0How to cite it
Christof Baumgärtel, Ray T. Smith, Simon Maher (2020) Accurately predicting electron beam deflections in fringing fields of a solenoid doi:10.1038/s41598-020-67596-0