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

For parameters that vary with time the trailing subscript a,b ,,, indicates the value of the parameter at the corresponding time. These time varying parameters that utilize these trailing subscripts include:
Time T;
Liquid lead inside radius Ri;
Liquid lead kinetic energy Ekl;
Plasma thermal energy Ep;
Number of deuterium ions Nd;
Number of tritium ions Nt;
Deuterium ion kinetic energy Ekd.

T = Ta at commencement of liquid lead acceleration;

T = Tb when liquid lead reaches its maximum inward radial velocity;

T = Tc when liquid lead reaches the gun muzzle at Ri ~ 2.0 m and when spheromak injection occurs;

T = Td when liquid lead forms closed shell at Ri = 1.45 m, fuel gas injection commences, Ekl = Ekld;

T = Te at end of fuel gas injection;

T = Tf at Ri = 1.0 m where plasma ions have kinetic energy of 7.5 eV

T = Tg at Ri = Rig where Ep = Epg = Ekld / 4

T = Th at Ri = Rih where Ep = Eph = Ekld / 2

T = Ti at Ri = Rii (minimum value of Ri) where Ep = Epi = Ekld + part of fusion energy

T = Tj at Ri = Rij where Ep = Epj = (Ekld / 2) + part of fusion energy

T = Tk at Ri = Rik where Ep = Epk = (Ekld / 4) + part of fusion energy

The initial liquid lead shell wall thickness at T = Td must be about Rid =5.2 mm. Fusion occurs at:
3 mm < Ri < 7 mm.
The initial liquid lead alloy velocity is about 300 m / s. Hence, for the system to work effectively the time of arrival of the pressure wave components should be accurate to much better than:
+/- (3 X 10^-3 m) / (300 m / s) = +/- 10 X 10^-6 s.

There are 212 pneumatic guns, so some statistical averaging will occur. Even so, the time of arrival needs to be accurate to within +/- 1.0 microsecond for every liquid lead slug. There are three major sources of arrival time error: error in the slug position Ric at T = Tc, error in the slug velocity (-dRi / dT) at T = Tc.

Assume that the time of is accurate to +/- 1.0 microseconds. Thus there is
+/- 1.0 microseconds available to accommodate slug position and slug velocity errors. Assume that the projectile has a velocity of 300 m / s. Then if the velocity error is zero the piston face must have an absolute position accuracy Dr given by:
+/- Dr = +/- (300 m / s) X (1.0 X 10^-6 s)
= +/- 300 X 10^-6 m
= +/- o.300 mm

If the position error is zero:
V dT + T dV = 0
dV = -V dT / T
T = D / V
Hence the maximum tolerable velocity error is:
dV = - V^2 dT / D
= -(300 m / s)^2 (1.0 X 10^-6 s) / .55 m
= 90,000 X 10^-6 m / s
= 9 X 10^-2 m / s

Thus the fractional velocity error is limited to:
(9 X 10^-2 m / s) / (300 m / s) = 3 X 10^-4

These tolerances that can be met using an interferometer type position sensor.

Hence the new technology challenge is to accurately control the liquid lead slug position and velocity as a function of time. The control coefficients will vary with the liquid lead slug mass.

Thus the Plasma Impact Fusion process is enabled by the availability of fast microcontrollers. The process requires about 235 such microcontrollers, connected in master-slave arrangement, of which about 218 microcontrollers are used for controlling the flywheel guns and the remaining microcontrollers serve functions such as master timing control, high voltage power supply control, plasma injector control, pneumatic storage control, capacitor bank control, vacuum system control, liquid lead pumping control, wall cooling control, injector port ball valve control, etc.

All the processors must have crystal controlled 20 MHz clocks and run on their own subject to an interrupt that frequently resynchronizes their real time clocks and subject to common serial control signals such as system stop that are routed from the master processor to all the slave processors. The system does not proceed with a gun firing sequence until all the slave processors report readiness to the master processor. All alarms from the slave controllers are routed through the master controller. The Master Controller is connected to a personal computer that provides a user friendly man-machine interface. There should be Master Processor software that allows easy examination and editing of all software and data stored in the slave processors via the central personal computer.

The PIF process is actually started by a signal from the port valve contol which determines the exact instant of spheromak injection.

Events are measured and controlled to within an absolute time accuracy of +/- 0.125 microseconds. This timing accuracy is achieved by synchronizing the real time clocks of all the microcontrollers via a common interrupt just before commencement of a firing sequence. An entire firing sequence is less than 0.125 second, so that provided that the crystal oscillators are all accurate to better than one part in 10^6, the slave processors real time clocks will remain adequately synchronized over the firing sequence period.

Assume that a frywheel gun rotor rotates at a velocity in the range 0 rev / s to 300 rev / s. Then in order to attain a +/- 0.125 microsecond timing accuracy the rotor position sensor must initiate a pulse every:
0.125 X 10^-6 s X 300 rev / s = 37.5 X 10^-6 rev.
To achieve this accuracy the rotor position sensor should count laser interference pattern changes from a mirro mounted near the flywheel hub.

The pulse rate will be at least:
(300 rev / s) / (37.5 X 10^-6 rev) ~ 10 MHz

Two optical sensors are required to obtain absolute flywheel angular position as well as the angular velocity indicated by the pulse rate.

Several preparatory steps must be completed before a firing sequence can commence. In each case the slave controller must do its job to manage the preparatory process and must report to the Master Controller when it is ready. These preparatory tasks include:
a) Achieving the desired pressure in the neutral gas injection system;
b) Achieving the desired plasma injector liner temperature;
c) Charging the capacitor bank(s) to the desired level;
d) Achieving the desired temperature in the circulated liquid lead alloy;
e) Achieving the required vacuum.

When the Master Controller has received system ready signals from all the slave processors the Master Controller requests that certain slaves transmit the most recent readings of common data to all the other slaves for use during the next firing sequence.

The Master Processor again polls all the slaves looking for readiness indicators from every slave. A location specific dianostic alarm must be generated if any slave indicates that it is not ready. The firing sequence cannot proceed until all such alarms are cleared.

The master processor then resynchronizes the real time clocks on all the slave processors.

The spheromak port injection valves and the flywheel guns are re-synchronized.

The master processor then sends a common control command that enables commencement of the firing sequence
on all the slave processors. All the slave processors are programmed to not proceed with the firing
sequence until they have received the firing sequence start command and sufficient time has passed on
their real time clocks to allow receipt of a firing sequence stop command.

The first action is to inject liquid lead into the hubs of the flywheel guns. These guns take a number of milliseconds to accelerate the liquid lead. The gun discharge must be very precisely controlled in real time. To the extent possible the liquid lead slug discharge velocity must also be precisely controlled.

The next action is trigger the high voltage power supply that forms the spheromak and compresses the spheromak through the plasma injector. The injection instant must be preciely controlled in real time.

The next action is to trigger various sensors that record the x-ray, gamma ray and neutron fluxes and transient pressures related to the fusion energy pulse.

The next action is for the Master Controller to send a common control signal to all the slave processors for them to do all necessary to prepare for the next firing sequence. If it is desired to shut the system down this signal is not sent. Instead a shutdown control signal is sent.

All slave processors should report a safe shut down condition before there is any assumption that a safe shutdown has been achieved. Alarms must be generated indicating the source of any problems that are preventing a complete safe shutdown. This system contains potential energy comparable to a main gun on a major WWII battleship, so there must be idiot proof redundant safety sensing and controls to avoid accidents.

The required timing accuracy cannot be realized by conventional PID control algorithms. Each flywheel gun control processor must store in memory the results from the previous few shots and modify its own internal control coefficients based on historical performance to realize the desired projectile arrival time accuracy. Each gun controller must have a 3 byte hardware counter that counts pulses from the flywheel angular position sensor and stores this count in memory versus time. Numerical analysis of this count pattern will indicate the position, velocity and acceleration of the flywheel. The related processor firmware must be written in machine language so that the exact timing between successive piston position counter writes to memory is known. The gun timing control routines will have to take into account variations in: liquid lead slu mass, liquid lead temperature, etc. There will need to be a secondary stepper motor control algorithm to achieve a fine level of impact timing control. The flywheel guns will have to cycle through a number of shots for the controller to learn the exact mechanical coefficients of that gun. These coefficients will gradually change with time due to equipment wear and variations in the liquid lead temperature/alloy mix.

The timing of the spheromak injection into the reaction chamber has to be precisely controlled relative to the flywheel gun and spheromak injector valve timing. The progress of the spheromaks through the plasma injectors will have to be recorded so that historical data can be used to align the spheromak injection timing with the flywheel gun and spheromak injector port valve timing.

The X-ray and gamma radiation emission as a function of time should be recorded because such a recording can be used to determine the compressed plasma radius and the liquid lead wall velocity at the instant of radiation emission.

The aforementioned firmware/software development in conjunction with the laboratory measurements necessary to obtain all the control coefficients will require several man-years of effort. Due to timing constraints much of the firmware must be written in assembly language. This is not a high level software project. This software must be extremely well documented. It will be processor specific, so careful thought needs to go into the selection of the microcontroller in terms of its long term availability and support, as well as its various hardware/software features. The microcontrollers are a relatively small fraction of the total system cost. The dominant cost is employee training and programming on that particular microcontroller. Ideally the same microcontroller hardware should be used throughout the PIF system. However, the software loaded into the different slave microcontrollers will be different. Simply keeping track of all the software versions and their mutual compatibility issues will be a major task.

This web page last updated April 3, 2015.

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