William W. Hansen was a giant of physics in the 1940s. His life was cut short, so his legacy is not well known, but his contributions to science have impacted the lives of countless people.
If you have ever visited the headquarters of Varian, you must take a road called Hansen Way. It is named after William Webster Hansen, the Stanford University physicist. He led a tragically short life, but without his work, radiotherapy would not be anything like it is today.
Starting in the 1920s and gaining steam in the 1930s, many physicists were working on the problem of high energy particle acceleration. Direct DC acceleration techniques were limited to energy gains of about an MeV or so, far below the 10s or 100s of MeV that were desired for research. This problem was a key motivator for Ernest Lawrence to develop the cyclotron, which he did at the University of California at Berkeley. Experiments with oscillating electromagnetic fields date back to Heinrich Hertz, and were a promising approach since they used the naturally occurring electric fields of the microwaves, removing the need to generate and control high voltages. But the microwave technologies of the time lacked the large powers needed for high energy particle acceleration. Recognizing the need to approach the problems differently, William Webster Hansen showed how to combine theoretical rigor with the practical ingenuity needed to solve the high energy problem in a most unique way.
Hansen realized that because radiation at the microwaves frequencies (GHz) would have wavelengths that would be about the same size as the waveguide that bounded them, for energy transfer to a charged particle to be possible, the oscillation period of the wave had to be made comparable to the desired transit period of the charged particle, which was not possible with standard oscillating cavities. The theoretical solutions for simple waveguides are not helpful for the complex shaped needed for practical waveguides, but this did not prevent Hansen from developing the concepts needed to understand energy transfer from the microwave radiation to the charged particle. His work helped the Varian brothers to invent the Klystron, and was foundational in building the two-mile accelerator for high energy research was built at Stanford University. In his wonderful book, Microwave Electronics, author John Slater credits Hansen as being the founder of this fascinating field of study.
Microwave tubes such as klystrons, magnetrons, and linear accelerators are incredibly clever devices. Their shape is designed to exploit the very large electric fields that come with high power microwaves. To transfer energy to the charged particle, the oscillating field can be manipulated with quite a bit of freedom so that the electric field can be synchronized with electrons travelling at the speed of light, enabling energy to be transferred. What is truly amazing about waveguide accelerators is that once they are built, there is no need to control any timing of fields or to control anything at all. All that is needed is a microwave source for the waveguide and electrons injected at one end. If the copper cavities have the correct shape, physics takes over and the energy transfer occurs as naturally and with the same certainty as an apple falling from a tree to the ground.
To illustrate this, the simulation shows a side coupled standing wave accelerator with electric field in the central cavities, and magnetic field in the side cavities. The red field is positive, so the electric field in the central cavities can accelerate an electron when the particle is synchronized with the field oscillations. When it cycles to a blue phase, the electric field goes negative, which won’t help the electrons gain energy.
There are several important concepts about how the accelerator works: 1) The microwaves move down the waveguide through the side cavities, which carry a magnetic field. 2) The side cavities also cycle between positive and negative magnetic field. When the electric field is at a maximum intensity, the magnetic field in the side cavities is zero, and vice versa. 3) As the electron transits the electric field cavity, the period of microwave oscillation matches the electron speed, which will be the speed of light for high energy particles. 4) It is because the electron speed is matched with the oscillation period (phase change) of the microwaves, that continuous energy gain is possible.
Hansen explained the how important physical concepts such as the shunt impedance, the Q factor, the group and phase velocities can be used to understand and develop this technology. For anyone who has studied Hansen’s work, his genius is obvious. Not only were his concepts critical for the Varian brothers in inventing the klystron, and the Stanford physicists in building their two-mile accelerator, but he was influential in helping the physicists working at the MIT Radiation Laboratory, who were leading the war effort to develop the magnetron based on the English design. This group of physicists included some of the most accomplished physicists in the twentieth century including several Nobel Prize winners, most notably, Hans Bethe. Not limiting himself to high energy particle acceleration, Hansen also collaborated with Felix Block on the discovery of Nuclear Magnetic Resonance, work for which Block shared the Nobel Prize in 1952.
Tragically, Hansen died of berylliosis and lung fibrosis just before his 40th birthday. Berylliosis is a chronic lung disease caused by exposure to beryllium, which Hansen used to construct his microwave devices as a PhD student.