PLASMA IMPACT FUSION

OVERVIEW

By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
Plasma Impact Fusion (PIF) is a technology for heat production and electricity generation via
deuterium-tritium thermonuclear fusion that may revolutionize the energy industry. This technology can
potentially provide all the benefits of nuclear energy while eliminating most of the hazards.

The Plasma Impact Fusion (PIF) process is in some ways similar to the Magnetized Target Fusion
(MTF) process under development by General Fusion Inc. in Burnaby, British Columbia.

This web page provides an overview of the Plasma Impact Fusion process. Other associated
web pages focus on specific parts of the PIF process.
 

PIF CONCEPT:
The PIF concept is to form a spherical liquid lead bubble approximately 3 m in diameter within a steel pressure
vessel. Inside that bubble is trapped up to 20 kJ of electromagnetic field energy. The field energy trapping
mechanism is a semi-stable plasma configurarion known as a spheromak. A spheromak with a magnetic field that
is primarily primarily poloidal is known as a Revered Field Configuration.

A balanced mixture of deuterium-tritium gas is injected into the liquid lead bubble. The injected
deuterium-tritium gas acquires energy from the spheromak and becomes a random deuterium-tritium
plasma.

A large external pressure, of the order of 10^8 Pascals, is briefly applied to the liquid lead bubble.
This external pressure transfers up to 10^8 J of kinetic energy to the liquid lead in the form of negative
radial momentum. As a result the liquid lead bubble under goes rapid radial collapse. This rapid radial
collapse causes adiabatic compression of the deuterium-tritium plasma. This adiabatic compression
causes an increase in both plasma temperature and density. Near the central impact point, Where the
inside radius of the liquid lead is less than 1.6 cm, deuterium-tritium fusion occurs.

The fusion reaction releases both high energy neutrons and high energy alpha particles. The neutrons
dissipate heat throughout the liquid lead and can be used for tritium breeding if a small fraction of
lithium is alloyed into the liquid lead. The high energy alpha particles will lose most of their energy
near the inner surface of the liquid lead, and hence will vaporize the inner liquid lead. This lead vapor
expands and is condensed via thermal exchange with the outer liquid lead. The liquid lead, which is
contaminated with various radioacive substances, is pumped through a helium-4 isolated heat exchanger
to safely produce hot steam and hence electricity.

The process of forming the liquid lead sphere containing a sphermak involves:
1) Forming a hollow liquid lead ellipsoid with open ends;
2) Forming a spheromak;
3) Compressing the spheromak;
4) Injecting the spheromak into the hollow liquid lead ellipsoid;
5) Closing the ends of the hollow liquid lead ellipsoid to form a hollow liquid lead sphere.

The first step in implementation of the PIF process is production of a suitable hydrogen isotope spheromak.
 

SPHEROMAKS:
There is a semi-stable plasma configuration that has both toroidal and poloidal magnetic fields. This
plasma configuration is referred to by physicists as a spheromak, a toroidal plasma, a ball plasma or
an electron spiral toroid. Spheromaks are described in detail on an
accompanying web page.

An example of a naturally occurring spheromak is ball lightning. With suitable equipment spheromaks
can be produced in a laboratory. There is a good photograph of a spheromak on the
General Fusion web site.

A spheromak of a particular net charge and a particular physical size has a characteristic total
energy Et. Decreasing a spheromak's size while holding its net charge Qs constant
increases its total energy Et.

The total energy Et is primarily composed of electric field energy and magnetic field energy
components. The electric field components arise from the spheromak's net charge. The magnetic field
components arise from spiral motion of circulating charged particles, primarily electrons.

For a particular net charge, total field energy and a number of free electrons there is an electron
velocity and hence an electron kinetic energy that results in a physically stable spheromak that can be
linearly compressed. There is a tradeoff between toroidal and poloidal magnetic field energy components
that affects spheromak shape.

Two suitably sized and magnetically oriented spheromaks can merge to form a slightly more stable
plasma with a mainly poloidal magnetic field. This merged plasma is known as a Field Reversed
Configuration (FRC).
 

PLASMA IMPACT FUSION (PIF) POWER PRODUCTION CONCEPT:
The steps to use of spheromaks for power production are:
 
1) To use a high efficiency electric plasma source axially centered within a 3.0 m inside diameter
cylindrical enclosure to produce a 2 kJ deuterium-tritium (D-T) spheromak having an equatorial
diameter of:
3.0 m / 2.71828 = 1.1 m
and circulating free electrons with a kinetic energy of about 13.5 eV.

This free electron kinetic energy is slightly below the impact ionization threshold for hydrogen
and hence is the maximimum free electron kinetic energy consistent with a very long spheromak lifetime;

2) To temporarily hold this spheromak at the upstream end of a conical plasma injector until the
vacuum system removes or absorbs the neutral hydrogen isotope molecules that are inadvertently injected
into the vacuum chamber during the spheromak formation process. This reduction in neutral gas
concentration is required to increase the lifetime of the spheromak after it is compressed;

3) To rapidly linearly compress the spheromak about 5X while keeping the spheromak's
net charge constant. This spheromak compression step increases the field energy of the spheromak
about 5X and increases the kinetic energy per free electron about 25X but reduces
the number of free electrons in the spheromak about 5X. The resulting compressed spheromak
has a field energy of about 10 kJ and has an equatorial diameter of about:
3 m / (5 X 2.71828) = 0.221 m
The reduction in the number of free electrons occurs via electron-ion recombination which increases
the concentration of neutral molecules surrounding the spheromak.

4) To simultaneously inject two such compressed spheromaks through axial ~ 0.60 m diameter
ports into a 3.0 m outside diameter ellipsoidal reaction chamber with liquid lead walls. The
reaction chamber is initially about 4.2 m long and is about 3.7 m long at the instant of spheromak
injection;

5) To merge the two compressed spheromaks in the reaction chamber to form a slightly more stable
plasma known as a Field Reversed Configuration (FRC) with a total energy of about 20 kJ;

6) To close the spheromak entry ports into the reaction chamber. While the ports are closing
the FRC loses about half its energy to the reaction chamber walls so that when the ports are fully
closed the FRC has a remaining energy of about 10 KJ and the reaction chamber is a sphere
with a 3.0 m outside diameter.;

7) To apply a large symmetrical external pressure to the reaction chamber's liquid lead walls to
cause the reaction chamber's inside radius Ri and inside volume:
(4 Pi Ri^3 / 3)
to rapidly shrink.

8) To inject into the fully closed and shrinking reaction chamber the appropriate number of D-T
gas molecules for optimum fusion power production. This neutral gas injection must occur before
the inside radius Ri of the reaction chamber collapses below:
Ria = 1.3 m
in order for subsequent adiabatic compression of the random plasma to provide sufficient plasma
heating to reach fusion conditions;

9) To transfer about 5 kJ of energy from the spheromak/FRC's electric and magnetic fields
to the D-T gas molecules inside the reaction chamber, thus forming a random plasma;

10) To adiabatically compress the random D-T plasma with
the high velocity spherically convergent liquid lead wall to
a radius Rib given by:
8 mm < Rib < 16 mm
and to a temperature of about 10,000 eV, as required to initiate thermo-nuclear fusion of
deuterium-tritium plasma;

The high mass ratio between the lead atoms and the deuterium and tritium atoms together with a high
negative radial velocity makes adiabatic compression of a random plasma from an ion kinetic energy of
~ 1 eV to an ion kinetic energy of ~ 10,000 eV theoretically possible. A spherically
converging liquid lead wall potentially provides the velocity, momentum and kinetic energy required
to achieve the required plasma ion density, ion kinetic energy and adiabatic confinement time.
At the instant of fusion ignition the liquid lead reaction chamber walls contain as much as 100 MJ
of kinetic energy.

11) To maintain the plasma temperature and density under adiabatic conditions long enough to meet the Lawson criterion for thermal nuclear fusion.

12) The liquid lead converts neutron and alpha particle kinetic energy into sensible heat, acts as a gamma ray shield and acts as a heat transport fluid for heat removal via an external heat exchanger. Lithium alloyed with the liquid lead is used for breeding more tritium (H-3) fusion fuel. There is an economically important breeding byproduct known as helium-3 (He-3).
 

THE PARTIES:
General Fusion Inc. (General Fusion) is a company based in Burnaby, British Columbia that is a developing a technology similar to that described above that General Fusion terms Magnetized Target Fusion (MTF).

THE PROCESS DEVELOPMENT CHRONOLOGY:
From a physics perspective there is little difference between Plasma Impact Fusion (PIF) and Magnetized Target Fusion (MTF). They are different names for two very similar processes aimed at obtaining nuclear energy from hydrogen and lithium isotopes. The General Fusion MTF process contemplated use of steam driven mechanical impact to accelerate a spherically convergent liquid lead wall to super sonic speeds. The MFI PIF process originally contemplated use of a high pressure low molecular weight inert gas to accelerate a spherically convergent liquid lead wall to super sonic speeds. Both processes relied on similar physics related to plasmas and thermonuclear reactions.

Prior to November 2012 the conceptual MTF process was simpler than the conceptual PIF process to implement but the MTF process had a high parasitic energy overhead that made its economics doubtful. The PIF process had better energy economics than the MTF process but the PIF process was more difficult to implement. Both processes had interstage timing issues.

In October 2012 this author identified that the spheromaks did not contain enough hydrogen isotope ions to provide the number of ions required by the subsequent fusion reaction. Hence neutral gas injection into the reaction chamber is required after spheromak injection into the reaction chamber to form a random plasma for adiabatic compression by the reaction chamber's liquid lead walls. Neutral gas cannot be injected earlier because it causes immediate spheromak randomization.

In mid-November 2012 this author identifed a modification to the MTF process that reduced its parasitic energy load. In effect the PIF and the MTF processes were merged into a single process under the PIF name, because PIF is more descriptive of the combined process. General Fusion was advised by email of the contemplated modified process on November 18, 2012.

In early December 2012 this author identified a major problem in the MTF/PIF process related to the compressed spheromak lifetime being shorter than the time required to close the reaction chamber's spheromak entry ports. In mid December 2012 this author identified the source of this problem as being neutral hydrogen isotope molecules that are inadvertently injected into the vacuum chamber during the spheromak formation and spheromak compression processes. In late December 2012 this author suggested a partial solution to this problem involving initial generation of a spheromak with an very low free electron kinetic energy (13.5 eV) to avoid impact ionization of surrounding neutral hydrogen isotope molecules.

In early January 2013 this author found that the plasma injector neck diameter needed to be increased from about 0.4 m to about 0.6 m to simultaneously meet both the electric field emission constraint issues in the neck of the plasma injector and the spheromak energy and lifetime requirements.

In mid January 2013 this author proposed use of temperature cycled uranium metal enclosure wall liner within the plasma injector to rapidly absorb neutral hydrogen molecules that are released during the spheromak formation and compression processes. These absorbed hydrogen isotope molecules are released from the uranium metal between fusion pulses by wall liner heating and are then extracted by the system vacuum pumps. The hydrogen isotope absorption equipment is essential to make the compressed spheromak lifetime long enough to enable complete reaction chamber port closure and liquid lead wall acceleration prior to spheromak randomization.
 

In early February 2013 this author found consistent closed form solutions to the liquid lead compression system's dimensional parameters.

CONCEPT INTEGRATION:
The individual Plasma Impact Fusion concepts are not new. These concepts were discussed within the physics department at Simon Fraser University during 1968. However, when the concepts were first conceived the electronics necessary for their successful implementation did not exist; the relevant material properties had not been investigated; the generation, electromagnetic structure and stability of spheromaks and FRCs were not well understood; and the equipment needed for hydrogen and helium isotope separation was not readily available.

Most of the steps in the PIF process have now been individually demonstrated at a laboratory scale. However, integrating these steps into a functional power plant remains to be done. This web site presents a mathematical model for the PIF process. However, there remain implementation challenges. Until the gross thermal output is actually measured the ultimate system capital cost per net electricity kW output will remain uncertain.
 

RISK:
From the perspective of this author the main area of development risk related to the PIF process lies in
the interstage timing. At this time there is insufficient information regarding the lifetime of
spheromaks to be certain that the various time constraints can be met. There is a time interval in
the range of 634 microseconds to 1268 microseconds between the time of injection of
compressed spheromaks into the reaction chamber and the time when the reaction chamber spheromak
entry ports are fully closed, permitting injection of hydrogen isotope gas into the reaction
chamber and subsequent adiabatic compression of the resulting random plasma. For the PIF process
to provide cost effective electric power generation the compressed spheromak/FRC lifetime must be
about twice as long as the time required to close the reaction chamber ports. This extended
compressed spheromak/FRC lifetime at spheromak free electron kinetic energies ~ 337 eV
has yet to be conclusively demonstrated.

As shown on the web page titled Reaction Chamber Port Valves
the time required for spheromak entry port closure is in the range 634 microseconds
to 1358 microseconds. There could easily be a problem with the compressed spheromak/FRC
lifetime being too short, in spite of various contemplated measures to extend the spheromak lifetime.

As shown on the web page titled Spheromak Generator
a high energy spheromak's lifetime is a function of the surrounding neutral gas concentration.
The neutral gas concentration as a funtion of time depends on the ion gun efficiency and the
vacuum system parameters. In order to produce a longer lifetime compressed spheromak it is
necessary to start with a very long lifetime low free electron kinetic energy spheromak. There
is very little reliable information in the published scientific literature relating to
production of very long lifetime high field energy (2 kJ) low free electron kinetic energy
(~13.5 eV) spheromaks. Such spheromaks are invisible because they do not cause ionization of
the surrounding gases.

In the past lifetimes of dimensionally smaller compressed spheromaks of about
80 microseconds have been reported but crucial data relating to the corresponding
concentration of neutral deuterium and other parameters is missing. In this author's view the
only way to conclusively resolve this spheromak/FRC lifetime issue is to build a pair of full
size spheromak generators and plasma injectors and experimentally measure the spheromak and FRC
lifetimes.

The contemplated reaction chamber port structures may have to be redesigned to meet the
experimentally determined spheromak life time constraints. It is already anticipated that it
will be necessary to change the reaction chamber external shape from spherical to ellipsoidal
to minimize the time required for reaction chamber port closure. The increase in plasma
injector neck inside diameter from 0.4 m to 0.6 m to reduce field emission
current will likely further increase the parasitic kinetic energy load.

Another source of risk that has not yet been addressed is safe absorption of liquid lead
alloy kinetic energy acquired due to vaporization of liquid lead and liquid lithium during the
fusion energy pulse. It may be very difficult to prevent high velocity liquid lead alloy droplets
damaging vqrious parts of this energy system. A related issue is potential difficulty
in fabricating the sphere, which must safely contain immense transient pressures.

Another source of risk that has not yet been addressed is degradation of the mass
ratio between lead and tritium due to presence of lithium alloyed into the lead.

Another potential source of risk is some problem in maintaining the required liquid lead
alloy wall thickness within the containment ellipsoid.

Another potential source of risk is problems realizing and maintaining vacuum seals in
the presence of the high temperatures and high impulse mechanical stresses
prevailing in this energy system.
 

H-3 AND He-3 BREEDING:
The plan is to use the neutron flux from the deuterium-tritium nuclear reaction to breed sufficient tritium (H-3) in a liquid lead-lithium alloy blanket to sustain the required tritium/helium-3 inventory. That breeding process will likely yield surplus helium-3 (He-3). The availability of this surplus He-3 may commercially enable Micro Fusion. He-3 also has other important applications in neutron detection and in medical imaging.
 

CRITICAL EVENT SEQUENCE:
In order for Plasma Impact Fusion to work a critical sequence of events must occur:

1) Synchronize the real time clocks of a large number of microcontrollers that are used for controlling functions such as plasma injector wall cooling, spheromak generation, spheromak compression, reaction chamber port closure, D-T gas injection, spherical compression and energy recovery. Most of these microcontrollers are used to precisely time the impacts of pneumatic pistons that are radially located all around the outside of a 3 m diameter by ~ 4 m long liquid lead ellipsoid that contains an axial vortex hole about 0.6 m diameter at the poles of the sphere. The hollow space is ~ 2.8 m in diameter near the equator of the ellipsoid. The impactor pistons are used to first close the reaction chamber ports and then to develop spherical convergent compression in the liquid lead. The motion of each impactor piston is controlled to achieve a precisely timed impact with a specific energy transfer.

2) The function of the liquid lead is to radially inward accelerate the liquid lead wall of the reaction chamber and its spheromak inlet ports inside the ellipsoid. The radial impact inertia of the liquid lead wall is responsible for the plasma compression to thermonuclear conditions. Hence the required impact pressure on the outside of the liquid lead ellipsoid is substantially less than the pressure required for direct fusion plasma confinement.

3) The initial velocity of the impact shock wave is the speed of sound (~ 2077 m / s) in liquid lead.

4) The incompressibility of the liquid lead above its own speed of sound in combination with spherical convergence is used to further increase the liquid lead wall's inward radial velocity to 16,374 m / s as the diameter of the hollow space within the liquid lead shrinks.

5) General Fusion, in its summary of the Magnetized Target Fusion process, contemplates use of high pressure steam to power the pneumatic pistons.

6) This author has a safety reservations related to direct use of high pressure steam with equipment containing large amounts of liquid lithium metal that is contaminated by radioactive H-3 and Be-7. For safety reasons this author prefers use of compressed He-4 for driving the impactor pistons.

7) A plasma producing device known as a spheromak generator, located at the upstream end of a conical evacuated enclosure known as a plasma injector, is fed a controlled quantity of a balanced mixture of DD, DT and TT gas molecules at a controlled rate;

8) Each plasma injector is 3.0 m inside diameter at its upstream end and is 0.60 m inside diameter at its downstream end;

9) A semi-stable confined molecular ion deuterium-tritium (D-T) plasma, known as a spheromak, is formed. This spheromak contains 13.5 eV kinetic energy free electrons, has an equatorial diameter of 1.104 m and has a field energy of about 2 kJ.

10) A spheromak contains an electron potential energy well trapped between poloidal and toroidal magnetic fields and cylindrical and spherical radial electric fields. At a free electron kinetic energy of 13.5 eV the free electrons do not impact ionize surrounding neutral hydrogen isotope gas molecules.

11) As long as the spheromak is attached to the spheromak generator the spheromak generator sets the value of the spheromak's voltage with respect to the enclosure. This voltage together with the enclosure radius determines the spheromak's external radial electric field. This external radial electric field value together with the enclosure radius Rc sets the spheromak's net charge Qs which in turn sets the spheromak's internal magnetic field energy. The required electron kinetic energy indirectly determines the number of free electrons.

12) After the spheromak has formed and while the free electrons in the spheromak have kinetic energies less than required to ionize the D-T gas the spheromak is held at the spheromak generator with the vacuum pumps running to remove D-T neutral gas molecules inadvertently injected during the spheromak formation process and hence increase the lifetime of the spheromak after it is compressed. This neutral gas removal process is enhanced by the use of a temperature controlled enclosure Wall liner that absorbs hydrogen isotopes at low temperatures and releases these isotopes at higher temperatures.

13) At this point it is assumed for calculation purposes that the spheromak equatorial radius is:
Rs = 0.550 m
and the local plasma injector inside radius is:
Rc = 1.50 m.

14) Before compression the spheromak should have a free electron kinetic energy of:
13.5 eV,

15) The enclosure wall liner is briefly cooled and then a spheromak is magnetically forced through the conical plasma injector, which reduces the spheromak's linear size. This process is analogous to adiabatic mechanical compression of a gas in an engine and hence is termed "spheromak compression".

16) The plasma injector consists of a long cone that reduces the spheromak's equatorial radius Rs about 5X while keeping the spheromak net charge Qs constant. As the spheromak's equatorial radius Rs decreases 5X its overall length (2 Hf) also decreases 5X, its axial magnetic field Ba increases about 25X, its total magnetic field energy Em increases 5X, and its free electron kinetic energy Eka increases about 25X.

Immediately after this linear spheromak compression the free electron kinetic energy in the spheromak core is about:
25 X 13.5 eV = 337 eV.
and the spheromak magnetic field energy is:
5 kJ
and the spheromak's electric field energy is:
5 kJ giving a total spheromak field energy of:
5 kJ + 5 kJ = 10 kJ

17) The plasma injector performs three essential functions. It increases the sphiromak field energy by a factor of 5, it increases the spheromak free electron kinetic energy by a factor of 25X and it reduces the sphiromak linear size by a factor of 5X. These three functions enable compressed spheromak injection for plasma preheating and compressed spheromak lifetime enhancement to permit reaction chamber port closure.

18) Increasing a spheromak's free electron kinetic energy increases the rate at which the spheromak's free electrons impact ionize surrounding neutral gas molecules and hence reduces the spheromak lifetime.

19) After compression a spheromak is immediately injected into a reaction chamber formed by a rotating liquid lead vortex. The inner face of this liquid lead is referred to herein as the liquid lead wall. This spheromak injection must occur while the internal radius Ri satisfies the inequality:
Ri > Ria.

20) Another similar spheromak, formed in another spheromak generator/plasma injector is simultaneously injected into the opposite end of the reaction chamber.

21) The two spheromaks are of equal size and are magnetically oriented so that they merge into one larger and slightly more stable plasma known as a Field Reversed Configuration (FRC). The toroidal magnetic components of the compressed spheromaks cancel so that the net magnetic field of the FRC is almost purely poloidal.

22) The impactor pistons strike the outside of the liquid lead ellipsoid near the reaction chamber ports initiating a cylindrically symmetric compression waves that close the reaction chamber ports. It is essential that the spheromak/FRC lifetime be substantially longer than the port closure time.

23) The remaining impactor pistons strike the outside of the liquid lead ellipsoid near its center causing formation of a spherically convergent liquid lead wall movement that compresses the contents of the reaction chamber. The liquid lead wall must reach the minimum inward radial velocity required for adiabatic compression prior to neutral gas injection at:
Ri = Ria
which causes spheromak/FRC randomization. The inward radial liquid lead wall velocity must increase as the plasma temperature increases.

24) Loss of the spheromaks/FRC field energy by neutral particle ionization during the reaction chamber port closure and wall acceleration time interval causes much of the spheromak's field energy to become kinetic energy in the approaching liquid lead wall;

25) The spheromaks do not transport enough hydrogen isotope molecules to meet fusion requirements. Hence at this point there must be a controlled insertion of neutral D-T gas into the reaction chamber to provide the appropriate number of hydrogen isotope nuclei. This neutral gas injection must occur while the internal radius Ri satisfies the inequality:
Ri > Ria.

26) These D-T gas molecules will immediately interact with the compressed spheromak/FRC and form a random plasma.

27) FUSION MOLECULE CONSTRAINT:
Define:
Nm = number of hydrogen isotope molecules actually participating in the fusion reaction;
Fr = fraction of hydrogen isotope molecules present that participate in the fusion reaction;
Then:
The number of hydrogen isotope molecules present in the reaction chamber at fusion ignition is:
(Nm / Fr)

For the D-T fusion reaction the gross energy output Epulse is given by:
Epulse = Nm X 17.6 MeV
 
General Fusion's design target is:
Epulse = 600 MJ
This target arises because if a pressure of 10^8 pascals is used to collapse the liquid lead system by a volume of 1 m^3 the parasitic pneumatic energy consumption is 10^8 J per fusion pulse. Assume that 3 units of heat are required to produce one unit of pneumatic energy. Then half of the gross thermal output is required to drive the parasitic load.

Thus the target value for Nm is:
Nm = (600 MJ / (17.6 MeV / molecule)) X (1 eV / (1.602 X 10^-19 J)
= 21.280 X 10^19 hydrogen isotope molecules.

28) NEUTRAL GAS SUPPLY:
In practice within one fusion pulse it is impossible to get all the D-T gas molecules in the reaction chamber to react. Hence:
Fr < 1.
The number of D-T molecules in the reaction chamber is 21.280 X 10^19 / Fr. If fraction Fr of this number actually reacts then the fusion energy pulse will be:
600 MJ

29) At 273 degrees K, 1 bar the approximate amount of D-T gas required to be injected into the reaction chamber is:
21.280 X 10^19 molecules X (22.4 lit/ mole) / (Fr X 6.023 X 10^23 molecules / mole)
= 79.143 X 10^-4 lit / Fr
= 7.9143 cm^3 / Fr

30) PARTICLE CONSTRAINT:
When a hydrogen isotope molecule fully ionizes it produces 4 particles, 2 free electrons and two atomic hydrogen isotope nuclei. Hence the total number of particles present in the reaction chamber is given by:
4 X 21.280 X 10^19 / Fr
= 85.12 X 10^19 / Fr

31) Upon neutral gas injection the spheromaks/FRC will quickly lose energy via impact ionization of neutral gas molecules. The rate of energy loss by a compressed spheromak/FRC to neutral gas molecules is high because the electrons in the compressed spheromak/FRC have sufficient kinetic energy to efficiently ionize neutral gas atoms. This creation of electron-ion pairs via impact ionization will quickly absorb the spheromaks/FRC field energy;

32) ENERGY APPORTIONMENT:
Define:
Rio = inside radius of reaction chamber when the liquid lead walls have no radial velocity;
Ria = inside radius of reaction chamber at the instant of neutral gas injection when the liquid lead walls have sufficient velocity to provide adiabatic compression of a random plasma.

The system design contemplates:
5 kJ
per spheromak of energy delivered to the random plasma after initial liquid lead wall acceleration. Hence in the random plasma the spheromak delivered energy per particle is:
[(2 spheromaks) X (5000 J / spheromak)] / (85.608 X 10^19 particles / Fr)
= [2 X 5000 J X Fr] / (85.12 X 10^19 particles)] X (1 eV / 1.602 X 10^-19 J)
= 73.33 Fr eV / particle

The strategy is to overheat the plasma. The plasma temperature will quickly drop until it reaches the temperature that is consistent with adiabatic compression at the velocity of the liquid lead wall.

33) Every hydrogen isotope molecule producing 4 particles receives an energy allocation of:
4 particles X 73.33 Fr ev / particle
= 293.336 Fr eV.
Included in this energy allocation are two hydrogen atom ionizations at:
13.6 eV / ionization
plus one hydrogen molecular bond break at:
4.5 eV.
Thus the remaining average initial kinetic energy Eki per particle prior to random plasma adiabatic compression by the liquid lead is given by:
Eki = [(293.336 Fr eV) - 2(13.6 eV) -4.5 eV] / 4
= 73.33 Fr eV - 7.925 eV.

If Fr = 1.0
then:
Eki = 65.41 eV

If Fr = 0.5
then:
Eki = 28.74 eV

If Fr = 0.25
then:
Eki = 10.41 eV

34) The limited average per particle kinetic energy Eki and the radius Ria are important constraints on the random plasma adiabatic compression. However, subject to sufficient delivered spheromak energy, the actual plasma temperature will be determined by the liquid lead wall velocity at Ri = Ria.

35) The result of spheromaks/FRC energy discharge will be a random neutral plasma with hot electrons. This plasma will be surrounded by a plasma charge sheath containing positive space charge that is balanced by an electron accumulation at the surface of the liquid lead wall. The voltage drop across this plasma sheath will be as necessary to reduce the hot electron momentum normal to the wall to zero at the liquid lead wall.

36) Positive ions that diffuse from the neutral plasma into the plasma sheath will be electrically accelerated across the plasma sheath to the liquid lead wall where they will be neutralized and will impact lead atoms and hence bounce back into the neutral plasma with high kinetic energy. By this means the ion temperature in the neutral plasma rises to the electron temperature. High kinetic energy ions in the neutral plasma should trigger D-T fusion reactions.

37) Both the plasma electrons and plasma ions must then acquire sufficient energy from the nearly adiabatic compression to reach average particle energies of 10,000 ev to enable fusion reactions. The energy content of the plasma at fusion ignition must be:
((85.608 X 10^19 particles / Fr) x 10,000 eV / particle X 1.602 X 10^-19 J /eV)
= (137.144 / Fr) X 10^4 J
= 1371.44 kJ / Fr.

Hence if the spheromaks deliver 10 kJ of energy to the plasma at the start of the adiabatic compression by the liquid lead, the liquid lead system must provide a plasma energy gain of:
(1371.44 kJ /(Fr 10 kJ) = (137.144 / Fr)
This energy gain can only be realized via random plasma compression. Spheromak compression simply does not provide sufficient plasma energy gain.

38) Once fusion reactions start high energy alpha particles released by the fusion reactions should further heat the plasma.

39) As shown on the web page titled SPHERICAL COMPRESSION, the liquid lead compression system requires about 100 MJ of kinetic energy per fusion pulse. The mechanical energy efficiency of this compression system is critical to the overall process success.

40) The high parasitic load imposed by the liquid lead means that the process is not self sustaining until the gross thermal output exceeds 300 MJ per fusion pulse. The presently planned maximum gross thermal output is 600 MJ per fusion pulse.

41) The adiabatic compression of the D-T plasma is maintained for over 0.5 microsecond to meet the Lawson Criterion for D-T thermonuclear fusion.

42) The resulting fusion energy release is violent. The fusion energy pressure pulse must be safely contained. Part of the liquid lead wall will vaporize due to high energy proton and alpha particle impact and will expand radially. The hot lead vapor must be cooled and condensed. The unreacted DD, DT and TT molecules and the He-4 molecules must be cooled, extracted, separated and recycled. The heat due to high energy neutron scattering must be removed. There is also heat release related to tritium and He-3 breeding and other nuclear reactions and decays. The heat is removed via a combination of liquid lead alloy and He-4 heat exchange.

43) There may be unresolved issues relating to liquid lead-lithium alloy and lead and lithium vapors blowing into the plasma injectors during a fusion energy pulse.

44) During the high pressure transient accompanying a fusion energy pulse, part of the fusion energy release should be captured by He-4 compression to assist in powering the pistons for the next liquid lead wall acceleration cycle.

45) All of the fusion pulse energy (~ 600 MJ) plus all of the lead compression energy (~100 MJ) needs to be absorbed as enthalpy by the liquid lead.
As shown on the web page titled ADIABATIC COMPRESSION the volume of liquid lead is approximately:
2.419 m^3 for Fr = 1.0 with a mass of 25.786 tonnes
1.208 m^3 for Fr = 0.5 with a mass of 12.877 tonnes
0.593 m^3 for Fr = 0.25 with a mass of 6.321 tonnes

The heat capacity of liquid lead is 26.65 J / mole-degree C

Hence the average temperature rise in the liquid lead per fusion pulse at Fr = 1 is:
[700 X 10^6 J] / [(26.65 J / mole-degree C) X (25.786 X 10^6 g) X (1 mole / 207.2 g)]
= 211.27 degrees C

Hence the average temperature rise in the liquid lead per fusion pulse at Fr = 0.5 is:
[700 X 10^6 J] / [(26.65 J / mole-degree C) X (12.877 X 10^6 g) X (1 mole / 207.2 g)]
= 422.64 degrees C

Hence the average temperature rise in the liquid lead per fusion pulse at Fr = 0.25 is:
[700 X 10^6 J] / [(26.65 J / mole-degree C) X (6.321 X 10^6 g) X (1 mole / 207.2 g)]
= 861.0 degrees C

It will require special heat exchanger design to accommodate these large temperature swings without thermal shock damage. These temperature swings may force a system power derating.

46) At the instant of fusion the thickness of lead around the fusing plasma is Rob which is given by:
Voll = (4 / 3) Pi Rob^3
or
Rob = (3 Voll / 4 Pi)^.333

For Fr = 1.0
: Rob = [(3 X 2.419 m^3) / (4 X 3.14159)]^.333
= [.577494 m^3]^.333
= 0.8327 m

47) Sufficient time must pass for completion of lead and lithium vapor condensation and vacuum extraction of unwanted gas molecules from the apparatus before formation of new spheromaks is initiated.
 

PROGRESS:
General Fusion Inc. has successfully developed an apparatus for producing and manipulating modest size spheromaks and is currently developing a larger diameter spheromak generator/plasma injector apparatus. General Fusion Inc. has successfully demonstrated the operation of the conical plasma injectors with an approximate 5X linear compression and an approximate 25X gain in spheromak free electron kinetic energy.

General Fusion Inc. contemplates merging two spheromaks within an ~ 1.0 m diameter quasi-spherical liquid lead vortex inside in a 3 m outside diameter liquid lead sphere and then adiabatically compressing the resulting FRC with high velocity spherically convergent liquid lead. General Fusion has developed a prototype liquid lead circulation system for realizing the required quasi-spherical liquid lead vortex.

Due to interaction with ionizable neutral gas atoms the lifetime of a spheromak or FRC decreases rapidly above a threshold electron kinetic energy. This decrease in spheromak lifetime at higher electron kinetic energies has been confirmed by experimental measurements at electron kinetic energies up to 300 eV. If the spheromak/FRC life time is too short there is not enough time for the reaction chamber ports to close and for the liquid lead wall to reach the minimum velocity required for adiabatic compression before the FRC discharges its field energy.

General Fusion has experimentally achieved an inward radial liquid lead wall velocity of:
4500 m / s
as compared to the velocity of sound in liquid lead of about:
2077 m / s.
Hence the liquid lead in spherical convergence behaves as an incompressible fluid above its own speed of sound.

When a random D-T plasma reaches an ion kinetic energy of 10,000 eV MFI has identified that the liquid lead wall inward radial velocity required for adiabatic compression is about 13,370 m/s. The highest published liquid lead wall velocity achieved by General Fusion to date using mechanical impact powered lead acceleration is 4500 m /s. Thus General Fusion's present liquid lead based plasma compression system requires further improvement.
 

CONSTRAINTS:
MFI has identified that the energy available for the fusion plasma at commencement of the adiabatic compression by the liquid lead is limited by the 5 kJ per spheromak of field energy remaining in each compressed spheromak.

A potential problem is sputtering of neutral lead atoms into the plasma due to impact by ~ 10 keV hydrogen isotope ions, which sputtering will occur if the liquid lead wall convergence velocity is not sufficient as the random plasma temperature rises. In this respect it is important to couple the correct amount of kinetic energy to the liquid lead. As shown on the web page titled Adiabatic Compression the adiabatic compression heating process only works as long as the number of particles enclosed by the liquid lead wall is constant. If due to lead sputtering the number of enclosed particles significantly increases the plasma will fail to reach fusion ignition temperature. Furthermore, lead ions then diffusing out of the plasma will rapidly lose kinetic energy to the liquid lead wall.

If there are too few D-T molecules in the reaction chamber lead sputtering, as described above, will occur. If there are too many D-T molecules in the reaction chamber they will not reach fusion ignition temperature at the calculated compressed radius. In theory they might react at a smaller compressed radius, but that assumes perfect impactor synchronization, which will not in reality occur. Having the correct number of D-T molecules trapped in the reaction chamber is important.

Practical issues related to economic fabrication and transport of the required fusion energy pulse containment pressure vessel limit its diameter to about 3 m.
 

PROJECTED PERFORMANCE:
The gross heat output is currently projected to be 600 MJ per fusion pulse. The best operating point in terms of net electricity production is a function of the efficiency with which kinetic energy is transferred to the liquid lead by the pneumatic impactors.

The timing of the pneumatic piston impactors has to be extremely precise.

Each fusion energy pulse results in a transient high gas/vapor pressure inside the containment pressure vessel. Practical issues related to vapor condensation and vacuum pump out of the pressure vessel between successive fusion pulses will limit the fusion pulse rate. This author believes that the target fusion pulse rate of one pulse per second mentioned on the General Fusion web site is over optimistic.

Once the system performance constraints are fully identified the equipment can be appropriately sized to maximize its performance and minimize its cost.
 

COMMERCIAL OPPORTUNITIES:
The obvious applications of Plasma Impact Fusion equipment are for distributed heat production and electricity generation. However, the equipment has an important byproduct that may also be quite lucrative.

At this time owners of nuclear fission reactors are not willing to commit to provide at a reasonable price the He-3 required to support Micro Fusion technology. The Plasma Impact Fusion apparatus is likely to produce substantial amounts of He-3 that is surplus to the operational requirements of an electricity generator and hence potentially available to support Micro Fusion technology.

He-3 is also needed for neutron detection and for medical imaging. Sensitive neutron detectors are needed for scanning vehicles and shipments for illicit neutron emitting fissile materials. Inhaled He-3 enables imaging of the lung blood vessels. The commercial value of He-3 has recently been in the neighbourhood of $10,000 per gram.

This author is of the view that General Fusion Inc. and Micro Fusion International Limited should try to come to a mutual accommodation because there is a substantial amount of common technology and because each needs the other for long term prosperity.
 

This web page last updated February 26, 2013.