Transcript Alpha Channeling in Centrifugal Mirror Machines

Wave induced supersonic
rotation in mirrors
Abraham Fetterman and Nathaniel Fisch
Princeton University
Outline
• Introduction to centrifugal confinement
• Advantages to driving rotation with
waves
• Computational results
Rotation is produced by crossed electric
and magnetic fields
Mirror coils
Fc
Fc||
E
Electrodes

B
Magnetic field lines
If we assume the potential is constant along a field line,
we find the rotation frequency is also constant, by
W
conservation of flux (particles are isorotating).
The confinement condition is then:
W
Lehnert B. Nucl. Fus. 11 485 (1971)
Conclusions
• Alpha particle energy can be used to maintain
the radial electric field by driving a current
volumetrically, eliminating the need for
electrodes.
• A group of waves was found and simulations
show 2.5 MeV may be recovered for each
resonant alpha particle.
• Using these waves, mirror devices with
supersonic rotation can be self-sustaining.
• Rotation in plasma centrifuges may also be
driven by waves
Supersonic rotation provides many
benefits to mirror traps
One finds by energy conservation, assuming
,
Thus the parallel energy confinement time,
Because the confining potential is much larger than the ion thermal energy,
the ion population is Maxwellian, and not subject to loss cone instabilities.
The centrifugal force is stabilizing to interchange modes for
Sheared rotation and parallel conductivity can also stabilize MHD modes.
Ionized neutrals enter the plasma with the rotation energy, providing a natural
heating mechanism.
Bekhtenev AA, et al, Nucl. Fus. 20 579 (1980),
Pastukhov VP, Rev Plasma Physics 13 203 (1987),
Lehnert B, Phys Scripta 13 317 (1976)
Volosov, V. Plasma Physics Rep 35 719 (2009).
Using endplates to drive rotation
introduces technical difficulties
Mirror coils
Dissipated current
Power
Source
Externally driven current
Electrodes
Magnetic field lines
•
•
Electrodes must support extremely high voltage drops (several million
volts overall)
Plasma density at the mirror throat must be sufficient to provide
conductivity between bulk plasma and electrodes
Driving the current volumetrically
eliminates some of these problems
Mirror coils
RF driven current
Dissipated current
Lines intersect
an insulator
Magnetic field lines
•
•
•
Field lines intersect an insulating surface
This surface can be designed to support high voltages and avoid
limitation by the Alfvén critical ionization velocity
There is no condition on conductivity between the bulk plasma and
mirror throat
Alpha channeling can be useful for rotating
plasmas
• The radial electric field provides an extra energy source/sink. We
want to convert alpha particle energy directly into electric potential
energy.
• Prompt loss of alpha particles is a benefit as in other fusion
devices: alpha particles take up plasma pressure that could be
used to confine fuel.
• To keep a low ambipolar potential, the electron temperature must
be kept low; alpha particles are an important electron heat source.
Regular alpha channeling
Wave
energy
Alphas
No waves
Tail ions
Rotation energy
Electrons
Fisch NJ Phys Rev Lett 97 225001 (2006)
Zhmoginov AI and Fisch NJ Phys Plasmas 15 042506 (2008)
Fuel ions
Alpha channeling in rotating mirrors
introduces the radial potential
In the frame rotating with the ions, the RF wave appears Doppler shifted,
The change in the particle’s midplane coordinates are then, including the
centrifugal potential,
r
The change in radius implies to a change
in lab-frame potential energy,
B
Fetterman AJ and Fisch NJ. Phys Rev Lett 101 205003 (2008)
Three options are apparent for energy
transfer
r0=0
~
W0
r0=rw
(b) Kinetic energy reduced and
potential energy increased; the wave
may be amplified or damped; the
particle may leave through loss cone
or at the outer wall.
(c)
(a)
(b)
W llres
(a) Kinetic and potential energy are
reduced; the wave is amplified; the
particle exits through the loss cone.
~
W||0
(c) Kinetic and potential energy are
increased; the wave is damped; the
particle is removed at the outer wall.
Paths (a) and (c) exist for a wave with positive phase velocity in the rotating
frame
. Path (b) requires a negative phase velocity.
Path (b) allows us to convert alpha particle energy to potential energy.
Fetterman AJ and Fisch NJ. Phys Rev Lett 101 205003 (2008)
Stationary perpendicular waves have a
branching ratio of 1
We define the branching ratio to be the ratio of potential energy gained to
kinetic energy lost. Assuming
Note that for waves that are stationary in the lab frame,
In order for the particle to satisfy the resonance condition
we must then use a wave with azimuthal mode number,
For practical values of  and c, this implies a mode
number of 20 or higher. The difficulty of launching
these modes is mitigated by the fact that the plasma
is localized near the cylinder boundary.
Fetterman AJ and Fisch NJ. Phys Rev Lett 101 205003 (2008)
Fetterman AJ and Fisch NJ. Phys Plasmas 17 042112 (2010)
so that
Multiple wave regions are used to cover
phase space
Phase space:
Real space:
Magnetic field lines
Alpha particle
birth energy
Loss cone
Device properties
Wave properties
Fetterman AJ and Fisch NJ. Phys Plasmas 17 042112 (2010)
The perturbation appears as a fast Alfvén
wave in rotating coordinates
In rotating coordinates, the stationary ripple
appears with a wave with,
The electromagnetic fields inside the plasma
are related to B1z, which is,
where kr is the solution to the two fluid cold
plasma dispersion relation. This solution is
matched to vacuum solutions and a current
layer at the wall.
Alpha particles are removed quickly
compared to the slowing down time
26% of particles exit promptly, 32% are removed by
alpha channeling in 1 s. The slowing down time is 4 s.
Alpha particles exit at low energy after
alpha channeling
Particles that undergo alpha channeling return 2.5 MeV to
the potential, or 64% of their total energy
Rotation may also be produced by waves
in plasma centrifuges
Stripping section Injection cell Enriching section
Heads (Product)
Tails (Waste)
•The separative power is proportional to
(rotation speed)^4
•Electrodes can react strongly with separation
products--removing them simplifies design
•Power consumption is comparable to gas
centrifuges
Fetterman AJ and Fisch NJ. Plasma Sources Sci Tech 18 045003 (2009)
In the rotating frame:
Drift
Rotation
Drag
Conclusions
• The concept of a branching ratio was developed to
describe the unique interaction of particles with the wave
and potential energy.
• Alpha particle energy can be used to drive a radial
current in centrifugal mirror machines, so that end
electrodes are not necessary for rotation.
• Simulation of a group of stationary waves shows that an
average of 2.5 MeV may be recovered per resonant
alpha particle, allowing a reactor to be self-sustaining.
• The branching ratio and alpha channeling concepts were
also applied to plasma centrifuges.
End
Power balance is achieved without end
electrodes
Consider an example reactor with the simulation parameters and L=40 m (not
optimized for power production)
Power recovered
Alpha particles lost:
radially (19%): 1.4 MeV,
axially (49%): 640 keV
channeled (32%): 2.5 MeV
550 kW
Axial fuel loss:
Deuterium: 320 keV
Tritium: 480 keV
440 kW
Power consumed
Fuel used for fusion
D: 400 keV, T: 600 keV
Fuel lost axially
-400 kW
-550 kW
Net power to potential
40 kW
Total fusion power: 9 MW
Particles that leave
axially must overcome
the centrifugal potential
and leave with less
rotation energy
Aspect ratio and centrifugal beta
The expression for beta is modified to include the centrifugal pressure,
The second term in this expression is proportional to the plasma size r0-r1, unlike
the first term. Thus, for fixed beta there is an optimum plasma layer thickness a.
Plasma cross
section at
midplane:
Fusion power production is maximum for
fixed beta if,
a
r1
r0
Bekhtenev AA, et al, Nucl. Fus. 20 579 (1980).
Lehnert B. Physica Scripta 9 229 (1974)
In rotating mirrors, the midplane
resonance depends on radius
The radius changes with
perpendicular energy as:
The resonant energy including centrifugal effects is:
r0=0
~
W0
r0=rw
Lines of
resonance
Diffusion
Path
Wllres
~
W||0
For perpendicular diffusion, the particle stays in resonance as it moves radially, but
diffusion paths are not parallel to resonance lines at fixed radius