Riemann's Contribution to Flight and Laser Fusion

The immediate context for the research was work on theaerodynamic problems of wing design and jet turbineconstruction for flight at supersonic speeds.The problem of supersonic flight had fascinated researchersand military thinkers since the first days of flight.But one outstanding feature of the problem had dominatedall considerations: At velocities greater than thespeed of sound, shock waves are generated. And theseshock waves, because of the nearly singular nature of theair disturbances they generate, make it difficult to maintainstable, controllable flight at supersonic velocities. Even so,the fabled Mach 1 (the Mach number is the ratio of thespeed of the aircraft to the speed of sound) was nearlyreached by a German airplane using jet engines in 1945—the ME-163, which reached Mach 0.86.Concentrating on the problem of the optimal design ofturbine blades, Busemann discovered during the Gottingen-Dresdenphase of his work some of the critical featuresof steady-state shock waves. The most famous of theresults of this research was his development of the Busemannbiplane, a configuration of two aircraft wings thatcompletely eliminates drag at supersonic speeds (see Figure1). Although this plane was never built, it had atremendous impact on the design of supersonic aircraft,on the scientific understanding of aerodynamic drag, andon the general problem of the propagation of shock wavesin two dimensions.The insight into Busemann's method provided by hiscomments in this interview is quite striking: His primarymotivation in the development of his theory was to eliminatethe inefficiencies in turbines. To accomplish thisend, Busemann realized that the properties of shocksupon reflection and turning were essential. This realizationled to the experiments and the analysis of schlierenphotographs of "dark spots" in the wind-tunnel flows.Using a quite intuitive geometric interpretation of themotion of the shock waves, Busemann realized that itshould be possible to completely eliminate the trailingshock lines if a set of "interfering" shocks could beproduced by a second wing. The Busemann biplane wasthe result.Out of this research, Busemann became interested inthe focusing of shock waves as well as their destructiveinterference. This extrapolation of his work on aerodynamicswas taken up in his work at the German rocketlaboratory at Peenemiinde just before and during WorldWar II. Busemann's comments on the Nazis' science programare revealing.As can be seen, the results of the work that Busemanndid during that period have had a tremendous influenceon the course of inertial confinement fusion research.Busemann wrote several papers on the focusing of shockwaves, partly as a study of how to avoid the concentrationof shock waves in flight and how to design "shapedcharges," configurations of chemical explosives that focusthe detonation of shock waves on a target. These papershave become essential ingredients in the design of advancedfusion fuel targets in inertial confinement fusion(see Figure 2). The energy concentrating capabilities ofthese configurations, especially Busemann's conical configuration,have led many researchers to expect that chemicalexplosives can be used to ignite a fusion reaction. Infact, a Polish team of scientists reported in 1978 that theyhad generated a significant number of fusion neutrons inan experiment using high explosives in Busemann's conicalconfiguration!After World War II, Busemann moved to the UnitedStates in 1947 and worked with NASA at Langley Field inVirginia. There, Busemann studied the aerodynamic forcesand surface heating of the starting and landing of spacevehicles, while his more famous colleague, Wernher vonBraun, designed the propulsion systems at NASA's Houstonresearch center. As a sideline of this work, Busemanndirected a seminar on electrodynamics, in the course ofwhich he made some critically important discoveries onthe existence and properties of magnetohydrodynamic(MHD) vortices. These vortices, which he compares totheir hydrodynamic analogues, have turned out to be acentral feature in most high-energy plasmas. In the pasttwo years, Busemann's work in this area has receivedrenewed interest because it is now thought that the fusionmachine that can most closely approximate the "natural"plasma vortex configuration will be the easiest to controland heat to ignition conditions. These new machine designs,like the spheromak and the reversed field pinch,are all variations on Busemann's MHD vortex.* * *Question: The Fusion Energy Foundation has done aconsiderable amount of historical research on Riemannand the Gottingen school of mathematical physics. Ourwork has shown over and over again that the work thatthe Gottingen school undertook was the most productive,containing the deepest insights into scientific questions offusion, for example. More recently, we have done somevery specific research on the role of shock waves andshock phenomena in laser fusion. Out of that work cameour attempt to do a new appreciation of Riemann's work.In doing that, we came across a whole series of researchesthat I think are largely unknown—in the United States, atleast—by yourself, Karl Guderley, and the people in Germanyin the 1920s, 1930s, and 1940s, researches that arenot appreciated in this country at all. A lot of currentresearch seems to be going through that same materialagain. What I would like to do in this discussion with youtoday is to get your insight into that history—why certainthings were done, what was done, and the importance ofthose things today.In the early years, in 1914, we already had a wind tunnelfor studying supersonic speeds. We saw a lot of blackthings in the photos that were not always shocks. Sometimesit was when the humidity of the air was high; thenthere would be some black spots on the photographs,too. But the important thing was the shock. In supersonicsituations, you cannot avoid getting shocks, no matterhow low the angle of the tip [the wing].This was already Prandtl's main interest at Gottingen.34 FUSION October-November 1981