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

This web page provides a step by step overview of the PIF process. Other associated web pages focus on specific parts of the PIF process and related theory.

There is a semi-stable plasma configuration that contains potential energy in the form of strong electric and magnetic fields. This plasma configuration is variously referred to by physicists as a spheromak, a toroidal plasma, a compact toroid or an electron spiral toroid. On this web site this semi-stable plasma configuration is referred to as a "spheromak". Understanding spheromaks is key to understanding the PIF process for achieving thermal nuclear fusion.

With suitable equipment spheromaks can be produced in a laboratory. Shown below is a photographic image of a spheromak published by General Fusion Inc.

PLASMA SPHEROMAKS are described in detail on an accompanying web page.

A spheromak with a particular net charge and a particular physical size has a characteristic total energy Et. Linear compression of a spheromak while holding its net charge Qs constant increases its total energy Et.

The total spheromak 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 distribution. The magnetic field components arise from the spiral motion of circulating ions and free electrons.

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

A spheromak exhibits a lifetime Ts after which it randomizes. This author believes that the spheromak lifetime Ts is primarily governed by impact ionization of neutral gas molecules by energetic spheromak free electrons and by electron emission from the enclosure walls.

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).

Theoretical maximum fusion energy / pulse = 1200 MJ
Nd = 4.258 X 10^20 = number of deuterium ions;
Nt = 4.258 X 10^20 = number of tritium ions;
Ric = 2.0 m = inside radius of gun muzzles;
Rid = 1.45 m = initial liquid lead shell inside radius;
(Rod - Rid) = 5.168 mm = initial liquid lead shell wall thickness;
Rie ~ 1.1 m = Ri value at which fuel injection is complete;
Rif= 1.0 m = Ri value at which plasma must have reached Eke = Ekd = Ekt;
Ekld = 65.5 MJ = initial liquid lead kinetic energy;
Ekdf = 3.5 eV = deuterium ion kinetic energy at Ri = Rif;
Ekd = Ekt = Eke = equal plasma energy distribution over particles for Ri < Rif
Ts = 2.0 ms = minimum spheromak lifetime
(- dRi / dT)|Rid = 300 m / s
Allowance for spheromak energy loss = 50%;
Spherical pressure vessel ID = 4.4 m
Spherical Pressure vessel wall thickness = .22 m
Gun Barrel OD = 16 inches = 0.4064 m
Gun Barrel ID = 14.688 inches = 0.3731 m
Gun Length = 6.0 m
Spheromak Injection tube length downstream from isolation valve ~ 3 m
Spheromak Injection tube wall thickness ~ 1.0 inch ~0.0254 m
Spheromak Injection tube ID = 0.60 m
Spheromak generator ID = 3.0 m

Liquid lead slug length at Rid is: 5.2 mm
Liquid lead slug equivalent diameter at Rid is: 16.71 mm

In order for Plasma Impact Fusion to work the following sequence of events must occur:

1) Synchronize the real time clocks of the large number of microcontrollers that are used for controlling functions such as spheromak generation, spheromak compression, injection port closure, deuterium gas injection, spherical radial compression and energy recovery. Most of these microcontrollers are used to precisely control the liquid lead flywheel guns that are used to form the 2.9 m inside diameter liquid lead spherical shell with radially converging walls.

2) A 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 deuterium gas molecules at a controlled rate. The quantity of injected deuterium is carefully regulated to prevent either too much deuterium or too little deuterium being injected into the vacuum chamber.

3) Each PIF plasma injector has a 3.0 m inside diameter at its upstream end and is 0.60 m inside diameter at its downstream end;

4) A semi-stable confined deuterium ion plasma, known as a spheromak, is formed. This spheromak contains about 30 eV kinetic energy free electrons, has an equatorial diameter of 1.104 m and has a field energy of about 600 J.

5) 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 30 eV the free electrons are able to impact ionize neutral deuterium gas molecules.

6) As long as the spheromak is attached to the spheromak generator the spheromak generator sets the value of the spheromak's equatorial plasma sheet 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.

7) The PIF process starts by formation of two spheromaks in separate 3.0 m inside diameter cylindrical vacuum chambers. Each uncompressed spheromak has a total field energy of about:
Etta = 600 J,
and has an equatorial diameter of:
2 Rsa = 3.0 m / 2.71828
= 1.104 m

and has number of free electrons:
Nea = 3.0 X 10^16 free electrons
each with a kinetic energy of about:
Ekea = 30.0 eV.
This free electron kinetic energy is above the impact ionization threshold for deuterium and hence will cause the spheromak to absorb all available deuterium atoms.

8) At this point in the PIF process it is assumed for calculation purposes that the spheromak equatorial radius Rsa at the upstream end of the plasma injector is given by:
Rsa = 0.550 m
and the local plasma injector inside radius is:
Rwa = 1.50 m.

9) Before compression the spheromak should have a free electron kinetic energy of 30.0 eV.

10) The spheromak is forced through the conical plasma injector by the axial electric field, 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".

11) 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 Bpc increases about 25X, its total magnetic field energy (Emp + Emt) increases 5X, and its free electron kinetic energy Eke increases about 25X. These spheromak parameter changes enable compressed spheromak injection into the spherical pressure vessel for heating injected deuterium gas and permit rapid injection port closure.

12) Immediately after this linear spheromak compression the free electron kinetic energy in the spheromak core is about:
25 X 30.0 eV = 750 eV.
This free electron kinetic energy is sufficient to cause impact ionization of any neutral gas molecule in this electron's path.

13) The compressed spheromak magnetic field energy is:
5 X 300 J = 1500 J
and the compressed spheromak's electric field energy is:
5 X 300 J = 1500 J giving a total compressed spheromak field energy of:
1500 J + 1500 J = 3000 J

14) After compression the spheromak has an equitorial diameter of:
2 Rsb = 1.104 m / 5
= .221 m
and has:
Neb = 6.0 X 10^15 free electrons

15) Spheromak compression reduces the number of free electrons and ions in a spheromak. The spheromak compression causes electron-ion pair recombination of spheromak component particles which increases the number of neutral molecules sharing the same vacuum chamber as the spheromak. The resulting neutral gas molecule concentration must be sufficiently small to meet the compressed spheromak lifetime constraints.

16) After compression a spheromak is immediately injected into the steel pressure vessel sphere. The spherical liquid lead shell is formed within the steel pressure vessel by converging liquid lead projectiles. The inner face of this liquid lead shell is referred to herein as the liquid lead wall. The spheromak injection must occur before
liquid lead obstructs the spheromak injection path.

17) Another similar spheromak, formed in another spheromak generator/plasma injector is simultaneously injected via the opposite end of the pressure vesssel.

18) The two spheromaks are injected through 0.6 m diameter axial ports into the top and bottom of a 4.4 m I.D., spherical pressure vessel. The O.D. of this spherical pressure vessel will be in the range 4.6 m to 5.0 m depending on the choice of materials and fittings.

19) The two spheromaks are of equal size and are magnetically oriented so that at the center of the spherical pressure vessel they merge into one larger and slightly more stable plasma known as a Field Reversed Configuration (FRC). The toroidal magnetic components of the two compressed spheromaks approximately cancel so that the net magnetic field of the FRC is almost purely poloidal. This FRC has an initial total field energy of about 3000 J.

20) The 0.6 m diameter axial ports into the spherical steel pressure vessel are closed with rapid acting ball valves. These valves with 0.6 m ports must move from fully open to fully closed in about 7 ms. These valves must be fully closed at the instant of fusion ignition and must be able to withstand the sprays of liquid lead alloy resulting from the fusion energy pressure pulses.

21) Around the spherical pressure vessel is a spherical array of 212 synchronized flywheel guns that fire 0.38 m (15 inch) diameter liquid lead projectiles, about 5.2 mm long on radially converging paths. These guns are timed to fractional microsecond accuracy. As the liquid lead projectile edges interact they collectively form a hollow spherical shell, enclosing the FRC with radially converging liquid lead walls. This shell has an initial inside diameter of about 2.9 m.

22) The liquid lead projectiles cause cylindrically symmetric liquid lead radially convergent compression. It is essential that the spheromak/FRC lifetime Ts be longer than the liquid lead shell formation time.

23) While the liquid lead shell is forming around the FRC the FRC must retain sufficient field energy, so that when the liquid lead shell is fully formed the FRC still has a remaining field energy of about 3000 J. At this point the liquid lead shell is aabout 2.9 m inside diameter with inside walls that have an initial negative radial velocity of:
(-dR / dT) = 300 m / s.
It is assumed that during this process the spheromaks/FRC retain at least 50% of their initial field energy.

24) The spheromaks/FRC do not contain enough deuterium ions to meet the fusion energy requirement. Hence, as soon as the liquid lead shell surface has formed additional deuterium-tritium gaseous fuel is injected into the liquid lead shell. This fuel injection must occur in the time interval Td < T < Te while the liquid lead shell inside radius Ri satisfies:
1.1 m < Ri < 1.45 m
in order for subsequent adiabatic compression of the random plasma to provide sufficient plasma heating to reach fusion conditions;

25) The energetic electrons in the contained spheromaks/FRC immediately impact ionize the injected deuterium gas and form a random deuterium plasma that absorbs about 3000 J of energy from the spheromak/FRC's electric and magnetic fields. This random plasma initially has high energy electrons and low energy ions.
Let Nd Frk be the number of deuterium molecules that actually react during a fusion pulse.
Let Epulse be the fusion energy release.

26) At 273 deg K, 1 bar the approximate volume of deuterium-tritium gas required to be injected into the reaction chamber is:
4.258 X 10^20 molecules X (22.4 lit / mole) / (6.023 X 10^23 molecules / mole)
= 15.836 X 10^-3 lit
= 15.836 mL

27) The immediate result of the spheromaks/FRC energy discharge will be a random neutral plasma with relatively hot electrons and relatively cool ions. This neutral plasma will be surrounded by a plasma sheath depleted in electrons. The voltage drop across this sheath will be equal to the average hot electon energy so as to reduce the electron momentum to zero at the lead wall.

28) 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 impact lead atoms and will bounce back into the neutral plasma with a high kinetic energy. By this means the ion temperature in the neutral plasma rises and the free electron kinetic energy falls. It is high kinetic energy ions that trigger deuterium fusion reactions.

29) The plasma adopts the effective temperature set by the negative radial velocity of the reaction chamber inside liquid lead wall. Then this negative radial velocity and hence the ion temperature rapidly increase as the contained volume enclosed by the liquid lead shell wall decreases.

30) The radial impact inertia of the liquid lead wall provides the energy that compresses and heats the plasma to fusion conditions.

31) The incompressibility of the liquid lead above its own speed of sound in combination with spherical radial convergence is used to increase the liquid lead wall's inward radial velocity as the diameter of the hollow space within the liquid lead sphere decreases.

32) The flywheel guns collectively provide about 65.5 MJ of kinetic energy to the liquid lead, in the form of negative radial momentum, causing a high negative liquid lead reaction chamber radial wall velocity and hence a rapid decrease of the contained volume within the liquid lead reaction chamber.

33) The negative radial inertia of the liquid lead walls causes the liquid lead shell's inside radius Ri and hence the inside volume:
(4 Pi Ri^3 / 3)
to rapidly shrink.

34) The rapid inside radius shrinkage of the liquid lead shell causes ADIABATIC COMPRESSION of the random deuterium-tritium plasma by the high velocity spherically convergent liquid lead shell wall to a radius of Rig = 7.54 mm at which point D-T fusion reactions commence.

35) The liquid lead shell exists for about 4.83 ms between initial shell closure and fusion ignition.

36) The high mass ratio between the liquid lead atoms and the deuterium-tritium atoms together with a high negative radial velocity makes adiabatic compression of a random plasma from an ion kinetic energy of 3.5 eV at Ri = Rif to an ion kinetic energy of ~ 120,000 eV at Ri = Rih possible. The spherical radially converging liquid lead wall provides the velocity, momentum and kinetic energy necessary to achieve the plasma ion density, ion kinetic energy and adiabatic confinement time that are required for deuterium-tritium fusion.

37) The resulting fusion energy release is violent. The fusion energy pressure pulse must be safely contained. The inner portion of the liquid lead wall will vaporize due to high energy alpha particle impacts and x-ray absorption and will expand radially causing a radial spray of the outer liquid lead. The lead vapor ultimately condenses via x-ray and thermal contact energy exchange with circulating liquid lead coolant which cools the inner walls of the spherical pressure vessel. The neutrons dissipate heat throughout the liquid lead.

38) The hot lead vapor must be cooled and condensed. The unreacted DD, DT and TT molecules and the He-4 molecules must be extracted, separated and recycled. The heat due to high energy neutron scattering must be removed and used for electricity generation. The heat is removed by pumping the liquid lead through an isolated heat exchanger.

39) The liquid lead converts both neutron and alpha particle kinetic energy into sensible heat, acts as a partial gamma ray shield and acts as a heat transport fluid. The hot liquid lead, which carries with it various radioactive substances is pumped through a liquid sodium isolated heat exchanger to safely produce hot steam and hence electricity via a two stage steam turbo-generator.

41) When the pressure in the spherical pressure vessel has decayed the 0.6 m diameter axial port ball valves on the spherical pressure vessel are opened, which enables vacuum extraction of unreacted gas and fusion reaction products.

P>42) The gun barrels are then drained in preparation for the next firing cycle.

43) The liquid lead gun injectors are then reloaded in preparation for triggering the next fusion reaction.

In each flywheel gun the liquid lead, which is in a high vacuum, is injected via a piston arrangement and then is accelerated by centrifugal force.

The temperature of the gun barrels is controlled to a setpoint sufficiently above the melting point of liquid lead alloy to minimize liquid lead condensation within the gun barrel while maintaining liquid lead surface tension. This temperature is the heat exchanger liquid lead discharge temperature.

Due to the axial spheromak insertion ports in the spherical pressure vessel there are no gun barrels directly on the sphere axis. To form the liquid lead sphere pole caps liquid lead is propelled from four smaller guns, each aimed at an angle to the polar radial path. In order to maintain the required spherical radial velocity component the muzzle velocity of these smaller near polar guns must be higher than the muzzle velocity of the other guns. Hence the near polar gun barrels may have to be be longer than the other gun barrels. The net liquid lead tangential momentum from these four smaller guns is zero.

This web page last updated April 3, 2015.

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