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

Plasma Impact Fusion (PIF) is a fusion based energy production process that involves conversion of deuterium and lithium into helium-4. The resulting liberated nuclear heat is intended for electricity generation. PIF can potentially provide most of the benefits of nuclear fission while eliminating most of the problems related to nuclear fission.

PIF involves electrical formation of a semi-stable high energy ordered plasma known as a spheromak, use of the spheromak to convert a confined deuterium-tritium gas mixture into a fully ionized random plasma, and use of the impact of a radially collapsing spherical liquid lead shell to adiabatically heat and compress the random plasma to fusion conditions. Hence the name Plasma Impact Fusion

The PIF concept involves marriage of five distinct technologies.
1. Electrical formation of deuterium (H-2) plasma spheromaks with energies of about 3000 J and lifetimes of about 2.0 ms;
2. Formation of a fully ionized confined random deuterium-tritium (H-2 + H-3) plasma by injection of a H-2 + H-3 gas mixture into a confined deuterium spheromak;
3. Adiabatic compression of the confined random (H-2 - H-3) plasma to fusion conditions using a spherically convergent high velocity liquid lead shell;
4. Breeding of sufficient H-3 to sustain the PIF process by using Li-7 to multiply the number of neutrons released by the (H-2 + H-3) fusions and then using Li-6 to capture the liberated neutrons and form more H-3.
5. Cryogenic separation of H-2 and H-3 from other gases.

The individual Plasma Impact Fusion concepts are not new. Some of 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; and the generation, electromagnetic structure and stability of spheromaks and FRCs were not well understood.

Most of the steps in the PIF process have 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 developmental challenges, especially related to extending the compressed spheromak lifetime. Until the PIF system net energy output is actually measured the ultimate system performance will remain uncertain.

There is a semi-stable ordered plasma configuration known as a "spheromak" that stores potential energy in the form of strong electric and magnetic fields. Spheromaks are also knoown as toroidal plasmas, compact toroids or electron spiral toroids. Understanding spheromaks is key to understanding the PIF process for achieving thermal nuclear fusion.

With suitable equipment plasma spheromaks can be produced in a laboratory.

During the period 2002 to 2012 General Fusion Inc. did important work on generation and compression of spheromaks. A photograph of a plasma spheromak produced by General Fusion Inc. is shown below.

PLASMA SPHEROMAKS are described in detail on accompanying web pages.

MFI hereby acknowledges receipt from General Fusion Inc. of quantitative measurements of typical spheromak parameters before and after spheromak compression. As set out on the web pages titled SPHEROMAK PROPERTIES and SPHEROMAK GENERATOR, this experimental data confirms almost all of the spheromak related theory that is presented on this web site.

The plasma hose and plasma sheet theory presented herein, which simplifies spheromak related calculations, is a special case of a more general mathematical theory developed by this author that relates quantization of radiant energy to quantization of charge in atomic particles. This theory expresses the Planck constant in terms of other physical parameters.

The total plasma spheromak energy Ett is composed of electric field energy, magnetic field energy and kinetic energy components. The electric field energy arises from the spheromak's net charge distribution. The magnetic field energy arises from the circulating electric current due to the spiral motions of free electrons and ions around a closed path.

For a particular spheromak net charge Qs, total field energy Ett and a number of free electrons Ne there is an electron velocity Ve and hence a free electron kinetic energy Eke that results in a physically stable spheromak that can be moved in space and that does not rely on external fields. The charged particle motion has toroidal and poloidal components that lead to spheromak regions with purely toroidal and purely poloidal magnetic fields. The relative strength of these magnetic fields determines the spheromak shape.

Linear compression of a spheromak while holding its net charge Qs constant increases the spheromak's total energy Ett.

A spheromak exhibits a lifetime Ts after which it spontaneously randomizes. This author believes that the spheromak lifetime Ts is governed by impact ionization of neutral gas molecules by energetic free electrons in the spheromak and by electron emission from the surrounding enclosure walls. This electron emission is a function of the electric field at the wall, the wall temperature and the wall material work function. Maximizing the spheromak lifetime is essential to the success of the PIF process.

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

In order to realize sufficient ion energy gain to attain fusion conditions from an adiabatic plasma compression by a liquid lead shell deuterium-tritium gas must first be fully ionized by energy absorption from spheromak(s) and the resulting deuterium-tritium plasma must be randomized.

An important issue is that when a spheromak randomizes the field energy contained in spheromak preferentially converts to plasma free electron kinetic energy instead of plasma ion kinetic energy. However, it is plasma ion kinetic energy that causes nuclear fusion. The issue of efficient transfer of free electron kinetic energy to random ion kinetic energy immediately prior to compression of the random plasma by the liquid lead needs careful attention.

The PIF process utilizes a combination of nuclear reactions which can be summarized by the formulas:
H-2 + H-3 = He-4 + n + 17.59 MeV
n + Li-7 = 2 n + Li-6
n + Li-6 = He-4 + H-3

In a real system only fraction Frk of the reactants actually fuse.

In order for the PIF reactions to run there must be energy feedback from the reaction products back into the reactants. The energy feedback is electrical rather than heat. Conversion of output heat into feedback electrical energy causes additional heat dissipation. At full rated load a PIF energy system produces about twice as much waste heat per kWhe of net electricity output as does a fission energy system.

A practical constraint on application of PIF technology is emission of vibration comparable to the vibration emitted by a very large shipboard diesel engine. Hence a PIF power plant is not suitable for installation in a dense urban environment.

The PIF operating sequence can be summarized by:
1) Generate two deuterium plasma spheromaks, each with an energy of about 3000 J;
2) Inject the two deuterium plasma spheromaks into a 4.4 m I.D. spherical pressure vessel;
3) Use an array of flywheel guns firing liquid lead slugs to form a 2.9 m I.D. spherical radially converging liquid lead shell around the spheromaks with initial kinetic energy Ekld = 65.5 MJ;
4) Use high speed ball valves to isolate the plasma injectors from the spherical pressure vessel:
5) Inject additional deuterium-tritium gas into the liquid lead shell;
6) Transfer stored energy from the spheromaks to the deuterium-tritium gas to form a fully ionized random deuterium-tritium plasma with a particle kinetic energy of about 3.5 eV;
7) Use the spherically converging liquid lead shell to adiabatically compress the random deuterium plasma to fusion conditions in the plasma radius range:
3.77 mm < Ri < 7.54 mm
Where the plasma thermal energy Ep is in the range:
Ekld > Ep > (Ekld / 4)
8) Maintain fusion conditions while at least 50% of the deuterium-tritium ions fuse;
9) Capture the released thermal energy by heating liquid lead from near its melting point to near its boiling point and by heating the thermal mass of the guns;
10) Allow sufficient time for hot lead vapor to condense;
11) Open the high speed spheromak injector port ball valves;
12) Vacuum extract all gases from the spherical pressure vessel;
13) Harvest the thermal energy by pumping the hot liquid lead through an external heat exchanger.
14) Convert the released thermal energy into electricity;
15) Reload the liquid lead guns;
16) Initiate the next PIF fusion pulse sequence.

Implementation of PIF requires that the energy and lifetime of the spheromaks injected into the pressure vessel in step (2) above be sufficient to allow implementation of step (3) above. The required minimum individual spheromak energy is about 3000 J and the required minimum spheromak lifetime is about 2.0 mS. Achieving these combined spheromak parameters is a technical challenge.

In order for the PIF process to function there must be efficient capture and storage of fusion pulse energy output and efficient conversion of the stored flywheel mechanical energy into liquid lead shell radially convergent kinetic energy.

Each fusion pulse nominally releases 600 MJ of nuclear energy. Part of this energy is dissipated as heat in the bulk of the liquid lead. The remainder of this energy vaporizes the inner surface of the liquid lead shell causing a pressure pulse that sprays the liquid lead outward toward the liquid lead gun muzzles and the inside walls of the spherical pressure vessel.

A practical PIF power reactor with a nominal gross thermal output of 600 MJ per fusion pulse is about 17 m diameter X 30 m high. The auxilliary equipment for vacuum pumping, extracted gas processing, high voltage electrical power supply and heat to electricity conversion is additional.

The web page titled: PIF PROCESS provides a detailed step by step review of the PIF process. Other associated web pages focus on specific parts of the PIF process and related theory.

Except where otherwise indicated, the intellectual property relating to the PIF process is property of this author, Xylene Power Ltd. and Micro Fusion International Ltd. (MFI).

There are four major technical developments required for successful implementation of the PIF process:
1) Develop a deuterium spheromak generator/injector that outputs 3000 J spheromaks through a 0.6 m diameter port with spheromak lifetimes of at least 2.0 ms;
2) Develop spheromak generator full port isolation ball valves with 0.6 m diameter ports and a closure time of less than 7 ms.
3) Develop a spherical liquid lead shell based random plasma adiabatic compression system with an initial liquid lead sphere inside radius of 1.45 m, an initial liquid lead shell wall thickness of 5.168 mm and an initial liquid lead radial velocity of - 300 m / s.
4) Develop the tritium fuel breeding system necessary to sustainably fuel the PIF reactor.

General Fusion Inc. is a company based in Burnaby, British Columbia that is attempting to develop a technology that General Fusion terms Magnetized Target Fusion (MTF).

Micro Fusion International Limited (MFI) is a company based in Ireland with engineering offices in Canada. MFI is responsible for the spheromak related theory and the PIF process development that are presented on this web site. Xylene Power Ltd. and MFI have spent the years since 2002 studying the physics, engineering, utility rates and business conditions that are required for successful implementation of Plasma Impact Fusion (PIF). The principals of MFI also have extensive experince in contracting, design, construction, operation and maintenance of small grid parallel electricity generation power plants.

The Plasma Impact Fusion (PIF) process is in some ways similar to the Magnetized Target Fusion (MTF) process that General Fusion Inc. of Burnaby, British Columbia, is attempting to develop.

An important distinction between the General Fusion Inc. MTF process and the Micro Fusion International Ltd. PIF process is that MTF relies on adiabatic compression of a spheromak by radially convergent liquid lead whereas PIF relies on use of the energy contained in the spheromaks to heat injected deuterium-tritium gas sufficiently to form a random plasma which is then adiabatically compressed by the high velocity spherically convergent liquid lead shell.

MTF relies on the spheromaks containing sufficient ions to fuel the fusion reaction whereas PIF relies on deuterium-tritium injection into the spherical liquid lead shell, after the liquid lead shell has closed around the spheromak(s), to fuel the fusion reaction. PIF relies on impact ionization of the injected deuterium-tritium by high kinetic energy free electrons in the spheromaks to trigger rapid and efficient energy transfer from the spheromak's electric and magnetic fields to electrons in the injected deuterium-tritium. These newly energized electrons then transfer their excess energy to the ions via wall interactions and a large number of random collisions.

MTF relies on steam driven pistons whereas PIF relies on electrically driven flywheel guns for liquid lead acceleration.

Another important distinction between MTF and PIF is that during the early part of the adiabatic compression by liquid lead MTF relies on persistence of the spheromak structure to prevent trapped ions leaking out along the spheromak injection axis of the MTF compressing liquid lead vortex. In contrast PIF avoids ion leakage along the spheromak injection axis by completely enclosing the spheromaks with a liquid lead shell before injecting the deuterium-tritium fuel and adiabatically compressing the resulting random plasma.

This author believes that the present General Fusion implementation of MTF will fail because of:
a) The practical material limitations involved with General Fusion's impactor technology:
b) Vapor pressure problems relating to use of lithium alloyed with lead, which General Fusion is relying upon for production of tritium;
c) Axial leakage of D-T ions along the spheromak injection axis, prior to complete closure of the liquid lead shell;
d) An insufficient number of D-T ions in the spheromak(s) to achieve the required fusion energy pulse output;
e) Low injected spheromak lifetimes in part due to high thermal electron emission from the conical plasma injector wall.

To avoid material fatigue, material wear and related safety problems that are implicit with General Fusion's use of steam driven impactors, the PIF process uses flywheel gun assembly of the spherically converging liquid lead shell. General Fusion reports an experimental impactor radial velocity of - 40 m / s whereas MFI anticipates achieving an initial liquid lead radial velocity of about - 300 m / s usong flywheel guns. This higher initial liquid lead shell closure velocity is is compatible with realistically achieveable spheromak lifetimes. The PIF process further contemplates use of a larger diameter plasma injector cone to further extend the lifetimes of the injected spheromak plasmas.

During the period 2002 to 2012 General Fusion Inc. did important work on generation and compression of spheromaks. General Fusion Inc. successfully developed an apparatus for producing and manipulating modest size spheromaks using an apparatus with a
Rwa = 0.5 m
upstream radius and a
Rwb = 0.1 m
downstram radius. General Fusion is currently working with a larger spheromak generator/plasma injector apparatus with a
Rwa = 1.0 m
upstream radius and a
Rwb = 0.2 m
downstream radius.

General Fusion Inc. has successfully demonstrated the operation of a half size conical plasma injector with a 4X to 5X linear compression and a 20X to 25X gain in spheromak trapped electron kinetic energy.

General Fusion Inc. has gathered experimental data that generally confirms the MFI spheromak theory set out on this web site.

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 General Fusion has demonstrated that liquid lead in radial convergence behaves as an incompressible fluid above its own speed of sound.

In General Fusion indicates that in 2012 it achieved an injected spheromak plasma lifetime of 600 microseconds at at a trapped electron kinetic energy of 100 eV. The corresponding poloidal magnetic field was about 0.4 T.

From an engineering perspective there are important differences between the Micro Fusion International Plasma Impact Fusion (PIF) process and the General Fusion Magnetized Target Fusion (MTF) process. Both processes are aimed at obtaining nuclear energy from deuterium-tritium fusion.

The General Fusion MTF process contemplates use of steam driven mechanical impactors to accelerate a spherically convergent liquid lead shell. The MFI PIF process contemplates use of compressed inert gas powered guns to provide the kinetic energy required to form the spherically convergent liquid lead shell.

The differences between the projected PIF and MTF processes are in part rooted in different interpretations of the electromagnetic structure and properties of spheromaks.

In October 2012 this author identified that practical spheromaks do not contain enough ions to provide the number of ions required by the subsequent fusion reaction. Hence, neutral deuterium-tritium injection into the liquid lead shell is required, after the liquid lead shell has formed and closed around the spheromaks, to provide the required quantity of random plasma ions for adiabatic compression by the radially converging liquid lead shell walls. A sufficient amount of neutral deuterium-tritium gas cannot be injected earlier because it causes immediate spheromak randomization.

In early December 2012 this author identified a potential problem in the PIF process related to the compressed spheromak lifetime being shorter than the time required to form the spherical liquid lead shell around the spheromaks. In mid December 2012 this author identified the source of this problem as being an excess of neutral deuterium molecules that are injected into the vacuum chamber during the spheromak formation and spheromak compression processes.

In early January 2013 this author found that the plasma injector neck should be enlarged from the 0.4 m adopted by General Fusion to about 0.6 m in diameter to simultaneously meet both the spheromak energy and lifetime requirements. The 0.6 m axial port size is also convenient from an equipment assembly perspective as it is sufficient to allow a man access to work inside the pressure vessel sphere.

In mid January 2013 this author recognized that extraction of recombined gas atoms resulting from spheromak compression is crtitical for obtaining sufficient spheromak lifetime to enable spherical liquid lead shell formation around the spheromaks prior to spheromak randomization.

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

In early March 2013 this author concluded that to keep the structural materials within their safe working stress limits the liquid lead spherical shell should be formed via synchronized gun assembly instead of by the liquid lead vortex method that has been pursued by General Fusion.

In late March 2013 this author recognized that one of the constraining elements of the PIF equipment design is the time required close the ball valves for the 0.6 m diameter axial spheromak injection ports in the pressure vessel sphere. This port closure is required to prevent high velocity liquid lead, sprayed by the the fusion energy pulses, from damaging the spheromak generation and compression apparatus. This port closure also reduces the lead vapor extraction by the vacuum system.

In early April 2013 this author concluded that the pneumatic gun propellant gas must be easily removed via a cryogenic trap. Hence He-4 is not suitable as a gun propellant. Argon, an inert gas with a higher condensation temperature, is much more suitable. Other inert gases with high condensation temperatures should also be considered.

In mid April 2013 this author found that improper interpretation of Thomson scattering and ion doppler data likely accounts for the discrepency in the number of spheromak free electrons between the MFI theory and the General Fusion experimental data.

In November 2013 this author found a closed form mathematical solution to certain spheromak related structural issues that may lead to further improvement of the PIF Process.

In late February 2014 this author found that the most practical methods of reducing the concentration of neutral gas atoms that limit the spheromak lifetime are to increase the efficiency of the spheromak generator ion gun so that there are less neutral gas atoms injected into the vacuum system and to enlarge the vacuum system volume. If Fg is the ion gun efficiency (nominally Fg = 0.1) and Volv is the evacuated volume (nominally Volv = 43.3 m^3 per spheromak) the product (Fg Volv) must be further increased about three fold to make the PIF system work as contemplated. The most elegant way of increasing the product (Fg Volv) is to increase the ion gun efficiency, but failing that then the vacuum chamber volume must be increased. Increasing the vacuum chamber volume increases the pump down time between fusion pulses, which reduces the return on invested capital, so further development work related to increasing the spheromak generator ion gun efficiency is justified.

In early November 2014 this author concluded that it is essential to configure the PIF system to operate with an initial liquid lead shell radial velocity of about - 300 m / s.

In January 2015 this author fouund an accurate closed form solution to the fusion integral, which quantifies the fraction of deuterium-tritium ions that actually react. It was found that only about half of the confined deuterium-tritium ions will fuse. This quantification further confirmed the requirement for an initial liquid lead velocity of - 300 m / s.

In March 2015 this author found a closed form expression relating the spheromak shape parameter:
So = (Rs / Rc)^0.5
to the charge hose winding ratio (Np / Nt). this relationship can be used for accurate determination of the total energy of a spheromak.

In early April 2015 this author determined that the best solution to the problem of energy efficient acceleration of liquid lead in a vacuum is to use flywheel guns. At a perimeter tangential velocity of 300 m / s such flywheel guns can be realized using presently available materials.

The net heat output is currently projected to be about 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 generated and transferred to the liquid lead shell and the efficiency of conversion of fusion pulse thermal energy into electrical energy.

The timing and muzzle velocity of the liquid lead guns must be extremely precisely controlled.

Each fusion energy pulse results in a transient high gas/vapor pressure inside the spherical pressure vessel and guns. Issues related to cooling 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 frequency of one pulse per second originally contemplated by General Fusion Inc. is over optimistic. In the near term an average fusion pulse frequency of one pulse per 10 seconds may be closer to reality.

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

A feature of a PIF nuclear fusion power system is that it is inherently modular. The average net power output from each module can be rapidly changed to track changes in the grid electricity load. If one module is shut down for service other modules at the same site can continue operating. Hence the overall system reliability is high, the load following ramp rate is high and the transmission costs are low making electrical kWhs output from distributed nuclear fusion reactors inherently more valuable than electrical kWhs output from centrally located nuclear fission reactors.

A fusion power system is inherently very safe because to sustain the fusion reaction there must be ongoing electrical or mechanical energy feedback. About 50% of the nuclear heat output from each fusion pulse is dedicated to triggering the next fusion pulse. Without this energy feedback fusion stops and hence there is no thermal output.

The disadvantage of this energy feedback requirement is that the capital cost of the heat to electricity conversion equipment per net electrical kWh of plant output is greater than the corresponding capital cost for a fission power plant. Similarly the cooling water requirement of a fusion power plant is greater than the cooling water requirement of a fission power plant with the same net electricity output.

As compared to a nuclear fission reactor a nuclear fusion reactor provides the following public safety advantages:
1) When a fusion reactor is shut down its heat output goes to zero.
2) Nuclear fusion reactors do not produce large inventories of long lived radio isotopes.
3) There are no reactor poisons (fission products) that limit the electrical load following capability of a nuclear fusion reactor.
4) If a terrorist attacks a nuclear fusion power plant there is little opportunity for causing damage outside the plant perimeter.
5) From a public safety perspective the security of nuclear materials inside a nuclear fusion power plant is almost a non-issue.

The combination of the aforementioned safety features allows deployment of distributed nuclear fusion power plants in remote areas with major cost savings in both labor and long distance electricity transmission.

The economics of a PIF system are governed by the system capital cost and the average net electricity output, which is proportional to both the net electrical energy output per fusion pulse and the fusion pulse frequency. The time interval between successive fusion pulses contains sequential time delays for condensation of lead vapor, draining hot liquid lead and re-establishing a high vacuum. Each of these sequential time delays may be several seconds in duration.

The total of these time delays determines the period between successive fusion pulses and hence the fusion pulse frequency.

The challenge is to make the fusion pulse frequency high enough to provide an adequate return on invested capital. Present estimates indicate that the capital cost and average electricity output of a PIF system are comparable to a small wind farm. However, a PIF system can be located much closer to the electricity load than most wind farms and the net electrical power output from a PIF system can be nearly constant. Hence a PIF system avoids high electricity transmission costs and the high balancing generation and/or energy storage costs associated with wind generation.

Fusion power makes economic sense to parties that recognize the following costs related to fission power systems:
a) Safety measures required to ensure safe removal of fission product decay heat;
b) Safety measures required to protect against malicious attack;
c) Safety measures required to prevent nuclear weapon proliferation;
d) Safety measures requred to protect against extreme environmental events such as earthquakes, tidal waves, hurricanes and floods;
e) The cost of power transmission from centrally located fission reactors to remote loads;
f) The cost of spent fission fuel disposal
g) The cost of supplementary generation triggered by inability of water moderated fission reactors to efficiently follow a rapidly changing grid load.

A significant power system design issue is that black start of a fusion power plant module requires an external power source comparable to the module's net electrical output capacity. This disadvantage can be mitigated by locating multiple fusion modules on the same site and starting them sequentially.

Another practical issue specific to fusion power systems incorporating liquid lead adiabatic plasma compression is output vibrations that are comparable to the vibrations emitted by the diesel engine of a large ship. These vibrations make this type of power plant unsuitable for installation in a dense urban area.

The obvious application of Plasma Impact Fusion equipment is for distributed electricity generation.

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 April 6, 2015.

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