Analog Science Fiction & Fact Magazine
"The Alternate View" columns of John G. Cramer 
Previous Column  Index Page  Next Column 

Weighing the Neutrino with Cyclotron Radiation

by John G. Cramer

Alternate View Column AV-176
Keywords: electron-neutrino, mass, measurement, tritium decay, cyclotron, radiation
Published in the March-2015 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 8/28/2014 and is copyrighted ©2014 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

    Measurement of the mass of the electron neutrino is one of the major unsolved problems of contemporary experimental physics. It is conventionally assumed that the e-neutrino is the lightest of the three neutrino types or "flavors" [electron (e), mu (m), and tau (t)], although other scenarios are possible. Neutrino oscillation observations have provided mass-squared differences between flavors, but the mass of the e-neutrino remains a missing piece of the puzzle. All three neutrino flavors are spin 1/2 leptons with zero electric charge and near-zero rest-mass. They come in matter and antimatter varieties and are usually created in weak-interaction processes in combination with their heavier cousins, the electrically charged e, m, and t leptons. Neutrinos interact with other matter only through the weak interaction and gravity. They are perhaps nature's most elusive particles and can pass through a light year of lead without a single interaction.

    Physicists usually discuss neutrino masses in units of electron-volts (or eV, where 1 eV = 1.783×10-36 kg). Because many neutrinos of all three flavors were produced in the early stages of the Big Bang, they could contributed significantly to the overall mass of the universe, so cosmology implies that the sum of masses of the three neutrino flavors must be less than about 0.3 eV. Data from neutrino oscillation observations implies that at least one of the neutrino flavors must have a mass of 0.04 eV or more.

    These estimates set the mass scale in which to look, but they are frustrating, because the present best attempt to directly measure the e-neutrino mass from the decay of tritium (3H, i.e., hydrogen-3) can only manage an upper limit of 2.2 eV, and even the planned KATRIN experiment, a large electric and magnetic tritium spectrograph being constructed in Karlsruhe, Germany, may be able to push this limit down only to about 0.2 eV. Thus there is a gap of at least a factor of 10 between what experimentalists are able to measure with currently available technology and the expected e-neutrino rest mass. A new measurement technique is clearly needed. Fortunately, a new technique pioneered by the Project 8 Collaboration has just appeared on the horizon, and we will describe this new approach in this column.

When a charged particle moves in a magnetic field, the magnetic force it experiences is perpendicular to both the magnetic field direction and to the particle's direction of motion. This typically causes the particle to travel in a spiral or circular path. At non-relativistic velocities the number of times per second (or frequency) that a particle in such a magnetic field completes one complete circle of this circular path does not depend on the speed or kinetic energy of the particle. This frequency fc= qB/2m, (with q=electric charge, B= magnetic field strength, and m=mass) is called the cyclotron frequency. E. O. Lawrence exploited the constancy of fc with energy to invent the cyclotron accelerator in the early 1930s. For the charged particles that Lawrence's cyclotrons accelerated, typically protons, deuterons, and alpha particles, the size of the circular path was a few meters and fc was around 10 MHz. However, for electrons the circles are smaller, the frequencies are higher, and relativistic effects are important.

    In particular, consider the tritium beta decay, which produces electrons forming a "bump" distribution of energies that cuts off at 18,600 eV (or 18.6 keV). The detailed shape of the cutoff at maximum energy of these electrons is affected by the e-neutrino mass, and this can be used to determine the e-neutrino's rest mass.  In a magnetic field of 1 tesla (or 1 T), an electron with an energy of 18.6 keV orbits in a circle with a radius of 0.46 millimeters. The classical cyclotron frequency fc of these electrons is 28.0 GHz, but because relativistic mass increase makes the electron more massive (and slower), the actual orbital frequency is f =27.0 GHz, a 3.57% shift downward in frequency. This frequency shift depends on kinetic energy, so that an accurate measurement of the orbital frequency would constitute an energy measurement, potentially one of high accuracy.

    When an electric charge is accelerated, it will radiate electromagnetic radiation. A single maximum-energy tritium beta-decay electron in its orbit in a 1 T magnetic field is a tiny antenna that will broadcast 27 GHz microwaves of cyclotron radiation with a radiated power of 1.2×10-15 watts, a power level that is quite detectable with modern electronics. Radiating away energy at this rate, the electron with a kinetic energy of 18.6 keV will lose energy at the rate of 7.5 eV per millisecond. Thus, in a 1 T magnetic field a maximum-energy electron from the beta decay of tritium should broadcast a detectable radio signal showing a characteristic rise in frequency as the kinetic energy is removed by the cyclotron radiation. This should be an unmistakable signal heralding the detection of a single electron and providing a measurement of its energy. However, we note that until the present work, the microwaves from such theoretically predicted electron cyclotron radiation had never been detected.

The Project 8 Collaboration is a group of experimentalists from six institutions, including MIT and the University of Washington. The group has constructed an experimental setup with a warm-bore 1 T superconducting magnet acting as an electron trap and containing a WR-42 K-band waveguide (a rectangular microwave transmission pipe with a cross-sectional area of 10.7 mm by 4.2 mm) into which a radioactive gas is introduced. The wave guide leads from the magnetic trap to a high-gain low-noise amplifier system designed to detect cyclotron radiation from radioactive decay electrons and to measure their frequencies and signal strengths.

    The first successful test of this system has just been reported. For the initial test, the waveguide contains the radioactive krypton noble-gas isotope 83mKr, a metastable gamma-emitting isomer of stable 83Kr, which has a half-life of 1.83 hours. In addition to gamma rays, 83mKr produces mono-energetic conversion electron "lines" with energies of 17.83 keV, 30.23 keV, 30.42 keV, 30.48 keV, and 31.94 keV. Cyclotron microwave radiation from all five of these electron lines has been observed and identified by the new system.

    Detection of single electrons is not easy. A remarkable figure in the paper shows a single 30 keV electron observed over a time period of about 5 milliseconds, during which its cyclotron radiation is seen to rise gradually in frequency for periods on the order of a millisecond, punctuated by more dramatic upward jumps in frequency as the electron scatters from background gas molecules (mainly hydrogen) in the system and loses about 13 eV of energy with each scattering. Thus, the non-destructive detection and measurement of electrons in an energy region that includes the 18.6 keV region of interest for tritium decays has been demonstrated.

Electron cyclotron radiation is a new tool for measuring the energy of electrons. The questions that remain are: (a) whether the low energy, (i. e, high cyclotron frequency) parts of the broad tritium beta decay spectrum can be excluded, in order to allow study of just the electrons near the spectrum's end-point, and (b) whether the energy resolution of the system can be improved enough to push into the mass region below 0.1 eV and make an actual measurement of the neutrino mass rather than just setting an upper limit. Other tritium-endpoint experiments have developed ways of restricting measurements to the electrons near the end-point, and this should be possible with the new technique. The system energy resolution depends on the accuracy with which the electron cyclotron frequency can be measured (mainly limited by noise and sampling time), and, because the measured frequency rises with time due to radiative energy loss, the accuracy with which the "start-point" of the signal can be determined. A 10 microsecond error in the determination of the start point would lead to an error of 0.075 eV in the extracted initial energy.

    The energy resolution of the Project 8 system in the initial tests is reported to be about 130 eV, which is certainly not good enough for extracting a determination of the e-neutrino mass. However, this is just the first step in this completely new frequency-based technique for detecting electrons and measuring their energy. The system resolution at this level is not restricted by any fundamental limits. Further, there is a well-known principle in experimental physics that the most accurate determinations of physical properties always involve the measurement of frequencies, so we can be optimistic.

    Watch this column for further developments in this area.

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


The Project 8 Collaboration results:
"Single electron detection and spectroscopy via relativistic cyclotron radiation", D. M. Asner, et al., arXiv preprint 1408.5362v1 [physics.ins-det], submitted to Physical Review Letters.

Previous Column  Index Page  Next Column 

Exit to the Analog Logo website.

 This page was created by John G. Cramer on 11/08/2014.