Physical Constants

Charge of the electron = 1.60217653E-19 C
Mass of the electron = 9.1093826E-28 g
Mass of the electron in amus = 5.4858990945E-4
Mass of the electron in Mev = 0.510998918 Mev
Mass of the proton = 1.67262171E-24 g
Mass of the proton in amu = 1.00727646688
Mass of the proton in Mev = 938.272029 Mev
Mass of 1 AMU = 1.66053886E-24 grams
Avgadros number = 6.0221415e23
Plank's Constant = 6.62606896E-34 J * sec
Plank's Constant = 4.13566733E-15 ev *sec
Room temperature atmosphere = 2.6867773E19 molecules/cm³
Energy 1 ev = 1.60217653E-19J/ev
Boltzman's Constant = 1.3806505E-23J/deg K
temperature deg K. = 11,604.505 times ev
Speed of light in vacuum = 299.792458E6 m/sec

I will be adding to this as requirements dictate and time allows.

Polywell - Making The Well

I have come across some interesting research by Kiyoshi Yoshikawaa,of the Institute of Advanced Energy, Kyoto University, and others proving the formation of the Polywell.

For those of you who have not been following along here is how my understanding has been evolving.

Polywell As I Currently Understand It

Polywell - Adding Details

A schematic of the evolution of the Polywell design can be found in slides 8 and 11 in this Power Point slide show (link at bottom of page).

In the Hirsh/Farnsworth machine in slide 8 the reacting positive ions (like charged Deuterium particles for one kind of operation) are attracted to the center to collide and produce fusions.

In the Elmore/Tuck/Watson machine in slide 11 electrons are accelerated to the center of the machine where they form a grid sort of like what happens in a beam power tube. In the beam power tube the virtual grid is called a space charge. These negative electrons attract the positive fuel ions and fusion reactions take place. The advantage is that there is no grid near the reaction space so losses are reduced.

That is the theory any way. However, in any person's mind who has a little understanding of the physics involved the question is: is that really happening? Are we fooling ourselves? Which brings us back to the Yoshikawa paper. What is the evidence?

Yoshikawaa correctly states the central issue:

...it is essential to clarify the mechanism of potential well formation (see Fig. 5) predicted to develop in the central plasma core within the cathode, since potential well formation due to space charge associated with spherically converging ion beams plays a key and essential role in the beam-beam colliding fusion, i.e., the major mechanism of the IECF devices. Actually, this has been the central key issue for IECF researchers for the past 30 years, until the first successful direct measurement of the double-well potential profile in the IECF device through the laser- induced fluorescence (LIF) method at Kyoto University [6] in 1999 with an approximately 200 V dip at the center in the helium plasma core as will be described below.

So they have proved the formation of the Polywell. Outstanding!

Many theoretical results so far predicted strongly localized potential well formation, and actually for the past 30 years, many experiments were dedicated to clarify this mechanism using, such as, electron beam reflection method [7], spatially collimated neutron [4] or proton [8,9] profile measurements, or an emissive probe [10], as is seen in Table 2, but, neither seems to be perfectly conclusive in convincing that well does form.

He again hits the nail on the head. Lots of results that could have more than one interpretation. He then gives a list of past attempts at verification of the Polywell. Now let us get to how what he claims was the definitive experiment was done.

...we have adopted optical diagnostics by using the Stark effects, sensitive to the local electric fields, to the IECF device with a hollow cathode. Also to enhance S/N (signal to noise) ratio as well as to specify radial potential profile, we introduced the LIF method. Consequently, we could have finally measured the double-well potential profile (see Fig. 11) with an approximately 200 V dip at the center for the first time in the helium plasma core (Fig. 7) in the IECF device.

He goes on in even more technical detail. The end result? The dual (cathode and anode) potential well forms.

In any future experimental regimes such a measuring system should be used to verify machine operation and to provide machine diagnostics.

Deriving Operating Voltage For An IEC Reactor

I have had some complaints (justifiable in my opinion) on how I derived the operating voltage for a given fusion reactor to within a few percent. I dont't take into account Einstein since the particle energies we are talking about for a proton are on the order of .6 Mev maximum and a proton "weighs" around 900 Mev. It might matter in the fifth place decimal (I estimate about a 1 part in 300,000 difference) but we don't really need to know the voltage that close since creation of the polywell will cost us around 10% of the drive voltage, indicating that any reasonable supply should be capable of about the calculated voltage +20% or maybe +25% to give a little more margin.

Well off to the races. First let me define the terms.

m₁ = mass of the lowest mass particle amu (protons)
m₂ = the other mass in amu
c₁ = the charge of m1 in electron charge units
c₂ = the charge of m2 in electron charge units
AV = accelerator voltage in KV
TV = the voltage from a chart or graph where one particle is stationary
V₁ = the velocity of m₁ when accelerated by AV
V₂ = the velocity of m₂ when accelerated by AV
V_1tv = the velocity of m₁ when accelerated by TV

V₁ + V₂ = V_1tv

When deriving the equations the = sign from now on will mean exactly proportional to.

m₁ * V₁² = c₁ * AV
m₂ * V₂² = c₂ * AV

m₁ * V_1tv² = c₁ * TV

Since we are using Newtonian mechanics velocities add:

V₁² = c₁ * AV / m₁
V₁ = √( c₁ * AV / m₁ )

V₂² = c₂ * AV / m₂
V₂ = √( c₂ * AV / m₂ )

V_1tv = √( c₁ * TV / m₁ )

I'm going to skip a few obvious steps here for brevity.

√( c₁ * TV / m₁ ) =

√ AV * ( √( c₁ / m₁ ) + √( c₂ / m₂ ))

√ AV = (√( c₁ * TV / m₁ )) / ( √( c₁ / m₁ ) + √( c₂ / m₂ ))

Which is in a spread sheet availabe at the IEC Fusion Newsgroup as an attachment.

Operating Voltage For B11

I want to work out the accelerating voltage for the B11 proton reaction.

From this excellent discussion of fusion reactions [pdf] we find that the optimum voltage for the p-B11 reaction when accelerating protons into B11 is 550 KV. Representing a proton energy of 550 Kev. However because we are accelerating protons and B11 from the same virtual grid voltage some adjustments must be made.

First off the reaction runs based on velocity not energy so we have to adjust the accelerating voltage to account for that.

The energy of a non-relativistic particle = 1/2 mV² However to keep from cluttering up the calculation we will throw out the 1/2 factor since we are not concerned with actual energy but just input voltage and for that the 1/2 cancels out. Masses will be given in Atomic Mass Units where the proton or neutron = 1. Also since we are not concerned with actual values but values relative to 550 Kev, energy will be given as Kev.

So let us start with proton velocity.

mV²=550Kev

Since the mass of a proton = 1 that simplifies to the required velocity = √550,000 = 741.6198 in arbitrary units.

For a given accelerating voltage the energy of the B11 will be 5X the energy of the proton because B11 has 5X the charge of a proton.

E_p=V_p²

E_B11=11*V_B²

V_p + V_B = √550,000

Since the energy of the B11 is 5X the energy of the p then

5*V_p² = 11*V_B²

V_p² = (11/5)*V_B²

V_p = (√(11/5))*V_B

V_p + V_B = √550,000

substituting:

(√(11/5))*V_B + V_B = √550,000

calculating the result

V_B = 298.650

V_p = 442.970

The energy of the proton will be:

442.970² = 196,222.175 or an accelerating voltage of about 200KV

The energy of the boron will be:

11 * 298.650² = 981,110.048

which when divided by 5 = 196,222.010 which checks within the accuracy of the numbers used.

Total energy required will be 1,177,332 ev or about 1.177 Mev

The Purpose Of IEC Fusion Technogy

The purpose of this blog is to collect and disseminate technical information on the design of components and systems for IEC Fusion.