E-Beam ICF for Daedalus Reconsidered

E-Beam ICF for Daedalus Reconsidered

Abstract

The Daedalus starship propulsion concept is electron-beam-driven inertial confinement fusion (ICF). Here I show that, without beam self-fields, the beam will form a large electron cloud and wonʼt set off the pellet. Even with optimal background plasma conditions, generating just the right self-fields, the beam suffers beamfront erosion, both inductive erosion and magnetic. They cause the Daedalus beam to erode away before reaching the pellet. I conclude that the Daedalus electron-beam ICF would not work.

 

Daedalus E-Beam ICF Concept

The Daedalus concept was based on the electron-beam-driven inertial confinement fusion (ICF) concept introduced by Friedwardt Winterberg around 1970. It was widely studied because intense particle beams were an entirely new field, which I joined in 1969 with relish. E-beam fusion peaked around the time of the BIS study; it didn’t last long. The reasons were primarily fuel pre-heat, but there were others. The Daedalus ICF geometry is a 100 m hemisphere [1]:

Fig. 1 Daedalus ICF reaction chamber

 

Figure 2. Cusp Field Geometry

Figure 2. Cusp Field Geometry

 

The magnetic geometry is a cusp. Large coils with axes parallel to that of the exhaust and counter wound to each other produce converging magnetic fields as shown in figure 2. The magnetic cusp was studied extensively in mid-20th century for plasma containment. The ring cusp is where the electron beams are generated. The spindle cusp is where the field lines converge above and below the plane of the beams. Properties of electron beams propagating in cusps has been little studied but the major features are quite apparent. Note that the field goes to zero on the axis where the pallet would be.

Propagating e-beams is hard.

If you inject into a vacuum the beam explodes by charge repulsion. If you inject into ionized plasma, the beam explodes because there are no fields to contain the transverse velocity component, and the more intense the beam is, the larger that component is. The only propagation regimes that work are either

1) strong guiding magnetic fields, either axial or azimuthal, in a background
plasma,

2) a partially ionized low-density medium wherein charge neutralization occurs
but current neutralization is only partial. This is called the ion-focused regime or IFR.

The problem with propagating e-beams in Daedalus is that the conditions in the reaction chamber are unlikely to allow propagation, much less concentration on the small pellet. The pellet explosion produces turbulent plasma that presses
against the magnetic field lines, and then is expelled into the exhaust. What remains? Probably a low-pressure plasma cooling off. Eventually a vacuum. This isnʼt treated in the Daedalus design, yet itʼs fundamental to whether the
scheme will work reliability at high repetition rate, hundreds of times per second, in a vibrating ship.

The propagation of electron beams injected into a cusp has 2 domains:

No Beam Self-Field

Suppose that there are no magnetic or electric fields from the electron beam. The electric field is neutralized by a background plasma (from the pellet explosion) or by collisions of electrons with neutral atoms, liberating the valence electrons. The magnetic field is canceled by a back-streaming return current. In this case, electron trajectories will look something like that of figure 3.

Fig. 3 E-beam trajectories in a cusp field

Fig. 3 E-beam trajectories in a cusp field

Electrons from the ring cusp bounce off the magnetic field lines and become randomized. Therefore, an electron sea fills the central region at a uniform density of electrons. There’s no concentration of electrons toward the pellet on axis. In fact, at the axis one would expect the electrons hitting the pellet to be isotropic. Needless to say, electron density will be greatly diminished because most of them will be nowhere near the pellet.

To estimate how big a volume the electrons will fill we need to know the magnetic field in that region. (The Martin-Bond paper on their Daedalus propulsion system says “the (transmission) lines are mounted around the exit of the chamber with the beam passing between the large field coils and along the field line to the target point.” In fact, there is little or no field line passing through the center of the cusp. The calculation in the paper of the field distribution is insufficient to tell what the field would really be like on the axis, but itʼs small.) The gyroradius of the electrons is 28 cm in the full 0.333 T field. My guesstimate of the diameter of the electron cloud is at least 1 m. The pellet is 4 cm diameter, so constitutes at most ~10-4 of the electron cloud volume. For all the electrons to pass through this small volume will take 100’s of microseconds. That’s if they donʼt escape the cusp field first.

I conclude that, without beam self-field, the beam won’t set off the pellet.

Some Beam Self-Field

 

Figure 4. Beam propagation erosion experiment.

Figure 4. Beam propagation erosion experiment.

When an electron beam is injected into a plasma channel, beam space charge repels channel electrons; the much more massive ions stay fixed. The positive ion channel then focuses and guides the electron beam. Electron beams
propagated in the IFR mode. This is also the regime where the key beam instability can be overcome: growth of transverse perturbations due to the hose instability. There are domains where this can be stabilized and, if not stabilized, at least its growth rate can be reduced.

However, even in this regime, there is a gradual loss of beam; this beamfront erosion happens for 2 reasons.

• Inductive erosion: as the beam propagates the ejected channel electrons form a radial current, inducing longitudinal electric field, which slows the electrons at the beam head. Which are then lost radially.

• Magnetic erosion: if any transverse magnetic field is present, there is a related reduction in focusing into the channel and a transverse Lorentz force loses electrons.

In 1994, a group at Sandia National Laboratories reported extensive experiments on beam propagation over 91 m propagating in the IFR mode [2]. This is roughly the diameter of the Daedalus chamber. I will summarize what their results imply for Daedalus.

Figure 4 shows the experiment. The background density was 3 x 10-5 Torr, ~10-8 atmosphere, a very low pressure. The plasma channel was formed by photo ionization from a KrF laser, 2-photon ionization process. Such a laser system is not included in Daedalus of course and would add to the mass of the system. Pulse duration was 800 ns, far longer than Daedalusʼ 25 ns.

 

Fig. 5. Erosion of a ~750 ns beam over 82 m.

Fig. 5. Erosion of a ~750 ns beam over 82 m.

 

Figure 5 shows the beam erosion over distance with the time axis corrected for time of flight. The beam front shows combined magnetic and inductive erosion as the beam propagates over 82 m. We can see that the Daedalus beam
would’ve been eroded away before reaching the pellet.

 

Fig. 6. Both magnetic and inductive beamfront erosion.

Fig. 6. Both magnetic and inductive beamfront erosion.

Quantitative measurements of the total erosion are given in figure 6, showing the effect of a transverse field. The lower line happened to have had the same transverse field as Daedalus, 0.033 T.

Daedalus electrons are launched parallel to the field lines, but as they approach the pellet, the field turns, as in Fig. 3, and becomes transverse. This data shows that, in a 30 m transverse field section, all of the 25 ns Daedalus electron beam pulse would be eroded away, due to magnetic erosion.

The experiments described here were conducted in the very best propagation regime to see how the electron beam would fare. They concluded that the losses were substantial for the leading edge of the beam, which is fatal of course for Daedalus.

Therefore, I conclude that the beams issued by Daedalus would have been completely eroded by the time they approach the pellet and would, like the no self-field case, become an electronic cloud in the center of the chamber. Then they would be lost into the spindle cusp.

 

Pulsed Power and Diodes

The pulsed power in the Daedalus design consists of a charging/start circuit, which transfers energy from the magnetic field in the reaction chamber to a charge circuit for a series of transmission lines, which then feed the diodes.

The charging system is a magnetic store/opening switch circuit for which the crucial element is the opening switch, which holds off 250 MV, opens in the timescale of 100ns and must operate for 10 billion repetitions. This capability is still far beyond any state-of-the-art in all parameters.

In the 21st century the method used for transmission lines would be an induction voltage adders (IVA), which is a method of connecting drive circuits in series of their voltages add [3]. The IVA is a much longer-lived method than transmission lines with closing switches. The lifetime of such systems can be greater than 100 million shots since the magnetic core switches have no internal discharges and very modest heating. They can maintain a high repetition rate easily above 1kHz. The only drawback is that they are heavier than transmission lines.

No diode design is given. The electron beams emitted around the ring have a current of 2.6 MA at a voltage of 237 MV. (The largest the highest voltage yet used in a pulsed system is 14 MV.) That gives that an electrical impedance of
about 30 ohms. If the beams are to propagate, they should not pinch, meaning that the self-field of the beam in the diode should not produce substantial transverse energy. Then the beam will tend to go straight. That requires that
each diode have a cathode of at least a meter diameter, in fact, several times that. Since there’s 6 m per diode around the 314 m circumference, and 50 diodes, this would be possible design.

Observations and a personal note

I conclude that the Daedalus e-beam ICF would not work. This was clear by the late 70s to those of us working in the field. But the Daedalus designers were not connected to the electron beam community by anything more than the rather tenuous theoretical approach of Winterberg. In fact, I never heard of the Daedalus study until after it was released.

This should teach us in Project Icarus to be very cautious about adventuresome projections. We would like a vigorous Icarus design, should we achieve it, to represent todayʼs state-of-the-art in a way unlikely to be obsolete in the nearterm. I feel we should take a serious look at magnetic fusion.

It’s been a pleasure for me to go back over the work I did 40 years ago on electron beam propagation and to remind myself of the many effects I struggled with in a host of experiments to try to propagate electron beams efficiently. For propagating beams against targets over distances, we eventually arrived at using strong guiding magnetic fields, either axial or azimuthal, in background plasma. This allowed it obligation very intense beams with little loss over distances of tens of meters. Was very Interested in this work; you can see the references (23 papers in 8 years!) at my website at the following address:

htpp://home.earthink.net/~jbenford/JB.htm

For e-beam ICF, the successor concept, ion beam-driven ICF, lasted much longer, until the imploded wire Z-pinch succeeded in producing X-ray radiation powers so high they can, if scaled, produce implosion of a ʻpillʼ of D-T to produce fusion. It now competes with lasers (the so-far unsuccessful NIF). By any measure of technical merit, the Z-pinch should win out. For fusioneers, this is nostalgic; Z’s were the first fusion concept (the gas discharge type) and now the wire version is likely to succeed, far more likely than the behemoth Tokamaks (the ITER).

References

[1] A. Martin and A. Bond, PROJECT DAEDALUS: THE PROPULSION SYSTEM,
Part 1; Theoretical considerations and calculations”, Project Daedalus- Final
Report, pp. S44-S62, 1978.
[2] P. W. Werner et al., “Erosion of a Relativistic Electron Beam Propagating in a
Plasma Channel”, Phys. Rev. Lett., 73, pg. 2986-2989, 1994.
[3] I. A. Smith, “Induction Voltage Adders and the Induction Accelerator Family”,
Phys. Rev. Sp. Topics-Accelerators and Beams, 7, 064801, 2004.