Physicists Discover Flaws in Bean’s Superconductor Theory

University of Houston physicists report finding major theoretical flaws in the “Bean” or “Critical State Model,” a generally accepted theoretical explanation of how a superconductor traps and holds a magnetic field. The team’s research, published in the Journal of Applied Physics, reveals unexpected new behaviors favorable to practical applications, including the development of energy-efficient ore separators, non-contact magnetic gears that will not wear or require repair, red blood separators with improved yield or even an automated docking system for spacecraft.

The basic property of a superconductor is that it represents zero “resistance” to electrical circuits. Superconductors consume zero energy and can store it for a long period of time. Those that store magnetic energy—known as trapped field magnets (TFM)—can behave like a magnet.

Much of modern technology is based on magnets, according to Roy Weinstein, coauthor of the research and professor of physics emeritus and research professor at the University of Houston. “Without magnets, we’d lack generators [electric lights and toasters], motors [municipal water supplies, ship engines], magnetrons [microwave ovens] and much more,” he says.

The Bean Model—developed more than 50 years ago by C.P. Bean, a scientist at General Electric, predicted, and until now experiments confirmed, that to push as much magnetic field as possible into a superconductor, the pulsed field must be at least twice as strong, and more typically over 3.2 times as strong as the resulting field of the trapped field magnet (TFM).

“Bean assumed the superconductor had zero resistance and that the basic laws of electromagnetism, developed circa 1850, were correct,” says Weinstein. “And he was able to predict how and where an external magnetic field would enter a superconductor.”

The performance of a device based on magnets generally improves as the strength of the magnet increases, up to the square of the increase. In other words, if a magnet is 25 times stronger, the device’s performance can range from 25 to 625 times better.

The method widely used today is to apply a magnetic field to a superconductor via a pulse field magnet after the superconductor is cooled. But this severely limits the applicability of TFMs, according to Weinstein. “It’s difficult and expensive to produce fields of more than 12 tesla. If Bean’s theory held true, this cost and practicality barrier would limit TFMs used within products to a maximum of typically 3.75 tesla.”

Weinstein says that his team has discovered that Bean’s model is far off base for certain constraints on a magnetic pulse and that a significantly different spatial distribution of field occurs. “Great increases in field occur suddenly, in a single leap, whereas Bean’s model predicts a steady, slow increase,” says Weinstein.

The team is still in the early stages of research but has already produced full-strength TFMs with a pulse strength 1.0 times that of the TFM. The researchers suggest this and other advances could in time enable scientists to replace a $100,000 low temperature superconducting magnet in a research X-ray machine with a $300 TFM or for engineers to replace a motor with one that is a quarter of the size of an existing one.

“A motor, if made in a fixed size, can produce 3.2 times the torque. Alternatively, the motor can be designed to produce the same amount of torque, but have its volume reduced by more than 10 times. This reduction in materials can result in great cost savings,” says Weinstein.

The Houston team is now searching for fast, short-term support that will allow them to continue their research to explain this new phenomenon. “While we now know enough to apply our new discovery to significantly improve a large number of devices,” Weinstein notes, “we don’t yet fully know what’s going on in terms of the basic laws of physics.”