Comment on “Observation of matter wave beat phenomena in the macrodomain for electrons moving along a magnetic field”

I show that the claim of the observation of matter wave beat phenomena in the classical macrodomain by Varma et al. [Phys. Rev. E 65, 026503 (2002)] is based on a mistaken interpretation of effects arising from multiple focusing of an electron beam in an axial magnetic field. I present the basic physical facts that mimic wavelike phenomena and suggest a classical explanation of modulations reported by Varma et al. Realization that the macroscopic “de Broglie wavelength” used by Varma et al. is the same as the focusing distance of a monoenergetic electron beam in the uniform magnetic field leads to a full classical explanation of all the effects reported by Varma et al. The reported observations are not evidence for any quantumlike phenomenon in the macrodomain, and their results do not indicate any violation of the Lorentz equation of motion.

Figure 1

The pseudo-standing-wave arising from multiple focusing of an electron beam in a magnetic field. The lower panel shows the shift in focal points when the energy of the beam is increased.

Figure 2

The variation of the current at the detector as a function of energy of the beam derived by assuming that the secondary electron emission (loss) depends on the intensity of the beam at the detector.

Figure 3

Current detected in an axial magnetic field when the secondary electron loss depends on the intensity at the detector and thus on the sharpness of the focus. The amplitude is smaller at lower energies due to the blur of the focus after the larger number of focusings before the electrons reach the detector.

Figure 4

The top panel shows the beats resulting from the addition of two classcal oscillatory currents. The bottom panel shows how the total current behaves when the difference in the frequencies of the oscillatory currents is large.

Figure 5

Classical model for the observation of beats by Varma et al. The physical inputs are classical focusings of the electron beam in the axial magnetic field and the intensity dependence of secondary electron emission from unbiased electrodes.

Figure 6

Results of the classical model plotted for the situation when the distance between the grid and plate is larger than half the distance between the source and plate. The agreement with the features observed by Varma et al. is very good.