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**INTRODUCTION:**

Simplistic theories of charged atomic particles represent the particles as point charges and point masses. Nuclei are often represented as having incident particle kinetic energy dependent absorption and scattering cross sections. In reality every particle has spacial distributions of both circulating charge and energy. The geometry of the charge distribution and the motion of the charge is such that there is no net force on the charge along its closed circulation path. A particle's spacial energy distribution may extend to infinity but its total energy is finite. Its net charge is quantized. Increasing the numbers of quantum charges contributing to the net charge increases the circulating current and hence the magnetic fields.

Conventional atomic particle theory is well summarized in the text: Physics for Radiation Protection.

The material contained on this web page involves application of spheromak theory to quantum charged atomic particles. Each such particle contains a spheromak which gives the particle its electromagnetic properties. Most of the particle mass is due to its spheromak magnetic fields. A small portion of the particle mass is due to the surrounding radial electric field. A neutron can be thought of as a superposition of a proton and an electron.

**ELECTRONS AND PROTONS:**

In our local universe energy is primarily concentrated in the rest mass of stable particles known as electrons and protons. Electrons and protons couple to form hydrogen atoms, which have a lower total energy than the sum of the energies of a free proton and a free electron.

The net charge on a proton is 1.60217657 X 10^-19 coulombs.

The net charge on an electron is - 1.60217657 X 10^-19 coulombs.

The rest mass of a proton in free space is 1.67262178 X 10^-27 kg.

The rest mass of an electron in free space is 9.10938291 X 10^-31 kg.

**ANTI-PARTICLES:**

There are corresponding charged particles known as anti-electrons (positrons) and anti-protons.

A positron has the same mass as an electron but opposite charge.

An anti-proton has the same mass as a proton but opposite charge.

These anti-particles are rare in our local universe.

**SPIN STATES:**

Spin is a charged particle parameter which is related to the direction of the spheromak poloidal magnetic field with respect to the the direction of an external magnetic field. For a specific poloidal magnetic field direction there are two possible toroidal magnetic field directions. In an atomic nucleus the nucleons tend to pair up so that their net external poloidal magnetic fields cancel. Similarly, in an atom the electrons tend to pair up so that their net external poloidal magnetic fields cancel. Field cancellation reduces the aggregate total energy and thus creates a mutual potential energy well. The combined electric and magnetic interactions between spheromaks in an atomic nucleus or in a solid creates numerous closely spaced energy states.

A free electron is generally indistinguishable from every other similarly oriented free electron except via its toroidal field orientation with respect to its axial field.

A free proton is generally indistinguishable from every other similarly oriented free proton except via its toroidal field orientation with respect to its axial field.

A free positron is generally indistinguishable from every other similarly oriented free positron except via its toroidal field orientation with respect to its axial field.

A free anti-proton is generally indistinguishable from every other similarly oriented free anti-proton except via its toroidal field orientation with respect to its axial field.

The afore mentioned distinguishing states are known as SPIN STATES.

**PAIR PRODUCTION AND ANNIHILATION:**

Under circumstances of a high gamma photon concentration and a low particle concentration a high energy photon can convert into an electron-positron pair. In circumstances of a high charged particle concentration and a low gamma photon concentration an electron and a positron can annihilate each other to form photons.

Under circumstances of a very high energy gamma photon concentration and a low particle concentration a very high energy gamma photon can convert into a proton-anti-proton pair. Under circumstances of a low gamma photon concentration and a high particle concentration a proton and an anti-proton will annhilate each other to form a new gamma photon.

There is an equilibrium between radiation energy density and particle concentration at which the rate of pair production equals the rate of pair annihilation. At this equilibrium the photons and the particles are said to be at the same temperature.

Our local universe has evolved to the point that, except in the cores of stars, the concentration of high energy gamma photons that can produce particle-anti-particle pairs is very low and the concentration of anti-particles is very low, so that particle generation and annihilation are no longer significant processes. However, cosmologists believe that the universe evolved from an initial high gamma photon concentration known as the "big bang". The high energy gamma photons formed charged particles. The charged particles then formed neutral hydrogen. The high concentration of free charged particles immediately prior to hydrogen formation prevents astronomers from observing earlier events via electromagnetic radiation.

**FREE NEUTRON:**

In the center of a star hydrogen atoms acquire sufficient additional energy that the electrons and protons join to form neutral semi-stable particles known as neutrons.
A free neutron contains slightly more energy than the sum of the energies of its major components, a proton and an electron. The net charge on a neutron is zero.

The rest mass of a neutron in free space is slightly more than the combined rest masses of a free proton plus a free electron.

Outside of an atomic nucleus a free neutron is unstable.

A free neutron has no net external electric field, which absence prevents normal electric field based spheromak wall stability.

Thermal neutrons have an apparent half life of about 11 minutes.

On neutron decay the additional energy forms a neutrino which conveys spin but no charge and which only rarely interacts with charged particle matter.

**BOUND NEUTRON:**

A neutron within an atomic nucleus can be viewed as consisting of a proton plus an electron plus some additional energy and opposed spin. Bound neutrons rely on the external fields from adjacent protons for long term stability. A neutron bound within an atomic nucleus has zero net charge and may or may not be stable.

**NEUTRON STRUCTURE:**

This author suspects that a free neutron is a an unstable structure including a positive spheromak (proton) and a negative spheromak (electron) sharing the same symmetry axis. The proton spheromak is much smaller and provides most of the neutron mass. The electron is larger and provides much of the particle magnetic moment. This structure lacks a stabilizing external electric field and hence is potentially unstable in free space. This structure can potentially be stable in a nucleus where other nearby particles provide external stabilizing electric and magnetic fields.

Consider two spheromaks, one inside the other, with opposite net quantum static charges, sharing a common axis of symmetry. The positive spheromak has much more energy than the negative spheromak and hence fits inside the core of the negative spheromak. The result is a seemingly neutral particle known as a neutron with a net external magnetic moment. This is the assumed structure of neutrons and anti-neutrons.

Experimentally a neutron contains more energy than a free proton plus a free electron.

**DEUTERONS:**

A deuteron is a stable combination of an electron and two protons.

The rest mass of a deuteron in free space is slightly less than the combined rest masses of a neutron plus a proton.

**ATOMIC NUCLEUS:**

An atomic nucleus can be viewed as being an assembly of protons, neutrons, deuterons and He-4 nuclei that are trapped within a mutual potential energy well. The mutual potential energy well is both deep and stable only at certain values of the number of protons and the number of neutrons. The depth of the potential energy well is characterized by its negative binding energy. When a nucleus absorbs or emits energy it usually does so via emission or absorption of stable or nearly stable particles such as photons, electrons, positrons, protons, neutrons or alpha particles (He-4 nuclei).

**NUCLEAR BINDING:**

Weak nuclear particle binding appears to involve spheromak to spheromak magnetic binding. Strong nuclear particle binding involves a change in the spheromak configuration.

**ATOMIC NUCLEI:**

A proton can magnetically bind to 0, 1 or 2 neutrons to form hydrogen, deuterium and tritium nuclei. A tritium nucleus is unstable and absent intense gamma ray radiation will spontaneously decay into a He-3 nucleus. An extremely stable combination is two protons plus two neutrons forming a He-4 nucleus. The He-4 nucleus has no net magnetic moment, indicating that its constituant particles are positioned such that all the individual magnetic moments cancel.

At very short ranges the magnetic field energy density of a spheromak exceeds the electric field energy density. A neutron's magnetic moment is similar to a proton's magnetic moment. Hence adjacent protons and neutrons in appropriate ratios can magnetically couple together.

If an electron sits between two protons it can reduce the electrostatic repulsion between the protons, enabling magnetic coupling and hence deuterium.

Binding mechanisms seem to account for the experimentally observed changes in nuclear magnetic moment and nuclear structure stability depending on the numbers of protons and neutrons in the observed atomic nuclei.

Atomic nuclei form first by formation of deuterons, then by combination of deuterons to form He-4 atoms, then by combination of He-4 atoms to form heavier atoms and then by capture of more neutrons and more deuterons. At each step in formation there is a gamma emission corresponing to the particle binding energy.

High atomic weight nuclei have a greater ratio of neutrons to protons than do lower atomic weight nuclei. It is this change in neutron to proton ratio that provides the potential for fission power because fission of a high atomic weight atom releases free neutrons that can support a chain rection.

**NATURAL RADIO ISOTOPE DECAY:**

An atomic nucleus consists of an assembly of charged particles. Atomic nuclei are only stable at certain proton to neutron ratios. If a nucleus can readily change into a similar assembly with a lower energy by emission of an electron, positron or alpha particle (He-4 nucleus) and/or a photon this change may spontaneously occur. Such a change is known as radio active decay. The time required for half of the nuclei of a particular isotope to spontaneously decay is known as that isotope's half life. The half life is a function of the isotopes binding potential well.

The range of possible decay paths is constrained by the requirement for compliance with the laws of conservation of energy, conservation of momentum and conservation of charge in any nuclear decay.

**ATOMIC NUCLEI **

In many atomic nuclei the binding energy for at least one neutron is insufficent to provide long term neutron stability. Hence the nucleus unstable.

Most unstable lower atomic weight nuclei decay by neutron decay which emits an electron (beta particle) and increases the atomic number by one, which improves the stability of the remaining neutrons.

Most unstable high atomic weight nuclei decay first by alpha particle emission and then a series of beta particle emissions.

Positrons are usually observed as a result of conversion of a nuclear energy decay that yields a > 1 MeV gamma photon which forms an energetic electron-positron pair. The positron is emitted while the electron joins a proton to form a neutron causing the net charge on the nucleus to decrease.

**FISSIONING**

A few unstable high atomic weight nuclei decay by neutron capture, fissioning and emitting more free neutrons to reach semi-stable fission product states.

**OTHER PARTICLES**

There are a large number of short lived particles (semi-stable energy states) that can be formed via high energy collisions between nuclei. However, these particles are short lived and have limited impact on the real world and hence are outside the scope of this web site.

**SPHEROMAK THEORY APPLICATION:**

Spheromak like structures enable the existence of stable elementary charged particles. In these particles net charge moves along a closed spiral path at the speed of light C and adopts a shape of a spheromak. A small part of the rest mass of each atomic particle comes from the energy contained within its spheromak's static electric and magnetic fields. Most of the particle rest mass is contained within the confined photon that circulates inside the spheromak wall. The externally observed quantum charge units behave as though they are themselves composed of opposite but unequal sub-quantum charges known as quarks. However, the quarks have never been observed in isolation an may only be mathematical constructs.

**SPHEROMAKS**

A spheromak is a stable quasi-toroidal electromagnetic structure comparable in shape to an axially elongated glazed doughnut. In the region inside the glaze the magnetic field is toroidal. In the region outside the glaze the magnetic field is poloidal. Viewed with the main axis of symmetry vertical the toroidal cross section is elliptical, about twice as high as it is wide. There is an electric current resulting from quantized net charge circulating at the speed of light along a closed path within the doughnut glaze layer. The net charge is quantized. The closed current path of length Lh has a uniform net charge per unit length and gives the particle its natural frequency:

Fh = C / Lh

This current path has an integer number Np of poloidal turns and an integer number Nt of toroidal turns. These integers are connected by the formula:

P = 2 Np + Nt

where P is a prime number.

The particle also contains Non-Electro-Magnetic (NEM) energy, which causes most of the particle's inertia and gravitation. NEM energy is formed from photon energy during production of of matter-antimatter particle pairs and reverts to photon energy during annihilation of matter-antimatter particle pairs.

Under normal circumstances there is no direct interaction between NEM energy and electromagnetic fields. All such field interactions are via the particle's spheromak.
However, NEM energy has a characteristic frequency Fn which determines the manner in which NEM energy interferes with itself as in the de Broglie dual slit experiment. This frequency is thought to be:

Fn = C / (2 Pi Ro)

where Ro is the nominal radius of the particle spheromak.

Note that Fn is about 3 orders of magnitude larger than Fh which is givenby:

Fh = C / Lh

where Lh is the length of the closed current path which characterizes a spheromak.
Thus:

Fn / Fh = [C / (2 Pi Ro)] / [C / Lh]

= [Lh / 2 Pi Ro]

which is a constant for spheromks.

**BACKGROUND:**

The electromagnetic properties of stable elementary charged particles such as electrons and protons with quantum net charges are due to formation of electromagnetic spheromaks. Electromagnetic spheromaks have energy associated with their electric and magnetic fields. The spheromak's electromagnetic field energy Ett contributes (Ett / C^2) to the particle's rest mass.

**ELEMENTARY PARTICLES:**

Elementary particles including electrons, protons and neutrons contain spheromaks. Typically quarks provide most of the particle rest mass and the spheromak provides the particle magnetic moment.

Note that for electrons and protons part of the energy that is internally contained in a neutron is contained in the external electric fields of electrons and protons.

A spheromak can be described in terms of a net quantum charge moving at the speed of light along a closed path containing Np poloidal turns and Nt toroidal turns. These integers Np and Nt together with the speed of light C, the permiability of free space Muo, the quantum charge Q and ellipse parameters precisely define the Planck constant h. The integer Np and Nt values also set the magnetic properties of quantum charged particle spheromaks. The spheromak linear dimension Ro is inversely proportional to the spheromak frequency Fh and the amount of electromagnetic field energy Ett contained in the spheromak.

Quantum charged particles have an electro-magnetic field energy component Ett that obeys:

Ett = h Fh

where:

h = Planck constant

and

Fh = natural frequency of the particle at energy Ett.

Spheromaks have quantized poloidal and toroidal magnetic fluxes. For a particular poloidal magnetic flux direction there are two equally possible toroidal flux directions. Much of quantum mechanics rests on the structure and behavior of spheromaks.

Chemical binding is largely due to far field interactions between spheromaks. The "weak" nuclear force is believed to be due to near field interactions between spheromaks. The apparent "strong" nuclear force is believed to be due to merging of spheromaks.

**CHARGED PARTICLE EXISTENCE:**

A free charged atomic particle, such as an electron or proton, is a nearly localized packet of energy with an electromagnetic energy component Ett which obeys:

Ett = h Fh.

The spheromak structure contains energy in the electric and magnetic fields due to circulating quantized net electric charge that continuously moves along a closed spiral path at the speed of light. The circulating current causes local toroidal and poloidal magnetic fields. The charge causes an external radial electric field. The closed charge motion path traces out a toroidal shaped surface referred to as the spheromak wall. The resulting electric and magnetic fields have an energy density and are stable in time and relative position. Integrating the field energy density over all space gives the spheromak's field energy contribution to the particle's rest energy. An isolated stable spheromak does not radiate photons. The field energy content of a spheromak as compared toa vacuum is inversely proportional to the spheromak's linear size.

**SPHEROMAK WALL POSITION:**

The circulating charge forms a charge and current sheet known as the spheromak wall. The position of the spheromak wall in space relative to the center of the spheromak is stable if at every point on this wall the total field energy density on one side of the wall is equal to the total field energy density on the other side of the wall and if at every point on the wall the position of the wall corresponds to a spheromak total energy minimum . These conditions define the physical shape of the spheromak wall and hence the closed spiral charge path.

**PHOTON ABSORPTION AND EMISSION:**

If a particle changes energy by absorption or emission of a photon it shifts from its initial spheromak state to a new spheromak state. In order for the particle's static field energy to increase the natural circulation frequency Fh of the spheromak must increase implying that the linear dimensions of the spheromak must decrease. In a stable spheromak the numbers of turns Np and Nt and the spheromak shape parameter So are all constants. The ratio:

(change in spheromak field energy Ett) / (change in charge circulation frequency Fh) = h

at the spheromaks stable operating point is known as the Planck constant.

The Planck constant is a function of other physical constants including: quantum charge Q, speed of light C and permiability of free space Muo and the inverse Fine Structure constant (1 / Alpha). The inverse Fine Structure Constant is a function of the number of charge circulation path toroidal turns Nt, the spheromak shape parameter So and an ellipse geometry constant [A / B].

**NUCLEAR MAGNETIC RESONANCE:**

The energy of a spheromak located in an externally applied magnetic field is dependent upon the orientation of the spheromak's axis of symmetry with respect to the axis of the applied magnetic field. A change in the orientation of the spheromak axis of symmetry with respect to the magnetic field axis is accompanied by emission or absorption of a photon. The frequency of that photon is proportional to the external magnetic field strength and the spheromak magnetic moment.

This phenomena is known as nuclear magnetic resonance (NMR). Hydrogen NMR has immense importance in biomedical magnetic imaging. However, NMR has limited general application because in heavier nuclei the magnetic moments of different nucleons tend to cancel each other.

There is an analogous effect with electrons in the magnetic fields of atoms that causes broad band emission of photons by thermally excited electrons, which is an important source of thermal radiation.

**PARTICLE SIZE AND PARTICLE REST MASS:**

The derivation of the Planck constant on this web site is independent of the spheromak nominal radius Ro and hence is independent of the total spheromak electromagnetic energy Ett.

If:

Rs = outside radius of spheromak wall with respect to the spheromak axis of symmetry;

Rc = inside radius of spheromak wall with respect to the spheromak axis of symmetry;

then the Planck constant depends on the parameter So where:

So^2 = (Rs / Rc)

but is independent of:

Ro = (A Rc So) = (A Rs / So)

Thus the Planck constant is the same for different energy particles such as electrons and protons that have the same quantum charge magnitude.

Work with Josephson junctions in superconducting materials indicates the existence of a magnetic flux quantum of:

Phio = h / (2 Q)

= 2.0678337 X 10^-15 Weber.

This magnetic flux quantum is an observed change in magnetic flux due to a single electron. To pursue this theory we develop on this web site accurate expressions for both the quantum spheromak poloidal magnetic flux and the quantum spheromak toroidal magnetic flux.

At this time, this author does not know the underlying mechanism of charge quantization. The magnetic flux quantization is simply a result of charge quantization and the laws of electrodynamics.

**SPHEROMAK INTERACTIONS:**

Charged particles that are separated by long distances interact via their overlapping electric fields. The change in total system potential energy due to the change in field overlap causes acceleration of the particles. However, when the distance between particles is small the situation becomes more complicated.

At shorter distances interaction due to overlap of the particle magnetic fields becomes important. At even closer distances particles may merge and in the process emit gamma photons. In addition some particle potential energy may convert into particle kinetic energy.

**CHARGE HOSE:**

A Charge hose is a mathematical construct that quantitatively explains experimentally observed atomic particle and plasma spheromak phenomena.

A quantum charged particle in a spheromak can be mathematically modelled as a long thin filament of circulating charge referred to herein as "charge hose". The charge hose naturally coils to form a quasi-toroidal shaped charge and current sheet known as a spheromak wall. The two charge hose ends are connected together to form a closed spiral path with length **Lh**. The charge hose forms the geometric divider wall of a stable electro-magnetic configuration known as a spheromak.

**CHARACTERISTIC FREQUENCY:**

Let C = speed of light. Then the time required for the net charge to propagate around the closed current path of length **Lh** gives the charged particle at rest a characteristic frequency **Fh** where:

**Fh = C / Lh**

Note that if the moving charge is composed of opposite charges moving in opposite directions the individual charge motion can be less than the speed of light whereas the apparent net charge flows at the speed of light.

For a given charge the smaller a spheromak is the more electromagnetic energy that it contains and the higher is its characteristic frequency **Fh**. If the spheromak's electromagnetic energy changes due to photon capture or photon emission while the spheromak's net charge remains constant there is a corresponding change in spheromak nominal radius Ro and hence there is a corresponding change in the spheromak's characteristic frequency **Fh**. The photon emitted or absorbed by the spheromak must reflect both the change in energy and the change in the charged particle natural frequency. The proportionality constant between the change in energy and the change in frequency Fh is known as the Planck constant **h**.

Note that the emitted or absorbed photon frequency Fp is approximately equal to the beat frequency difference between the initial particle natural frequency **Fha** and the final particle natural frequency **Fhb**. Thus:

Fp = |Fhb - Fha|

Note that during this configuration change a small amount of energy may be converted into kinetic energy related to particle recoil momentum.

**ENERGY STABILITY:**

As long as the net charge is uniformly distributed along the length of the current path and moves at a uniform speed C along the current path, and as long as the current path is geometrically and dimensionally stable, there is no change in the spacial distribution of charge with time and hence there is no change in field geometry or field energy. Hence there is no emitted or absorbed electro-magnetic radiation and the particle is stable.

**DISCRETE SOLUTIONS:**

There is a further aspect of the current path that is important in quantum mechanics. The number of poloidal turns **Np** and the number of toroidal turns **Nt** must both be exact integers.

**CHARGED PARTICLE MODEL:**

The following structure summarizes my understanding of the physical properties of simple charged particles.

Each free charged particle contains a spheromak. Each spheromak can be viewed as a quantum of charge that is uniformly distributed along a closed complex spiral path. The net charge motion along this spiral path is at speed of light C. The period required for the net charge to cycle around the closed path length Lh at the speed of light C has a corresponding frequency Fh which gives the spheromak a characteristic frequency. The spheromaks' electric and magnetic field energies make a small contribution to the particle's rest mass energy.

The closed spiral charge path forms a quasi-toroidal shaped charge and current sheet known as the spheromak wall. Inside the spheromak wall the field is purely magnetic and is purely toroidal. Outside the spheromak wall the magnetic field is poloidal and the electric field is radial. Due to the closed spiral current path geometry the charge per unit area on the spheromak wall varies with the radius from the spheromak's main axis of symmetry. Outside the spheromak wall the total energy density **U** takes the form:

**U = Uo [Ro^2 / (Ro^2 + (A R)^2 + (B Z)^2)]^2**

where:

**Uo** = a single spheromak peak energy density;

**Ro** = a characteristic radius from the spheromak's main axis of symetry which determines the spheromak's contained energy;

**R** = radius of a point from the spheromak's main axis of symmetry;

**Z** = distance of a point from the spheromak's equitorial plane.

**A / B**= (ellipse major axis parallel to Z axis) / (ellipse minor axis)

Define:

**Rc** = inner radius of spheromak wall on the spheromak equatorial plane

**Rs** = outside radius of spheromak wall on the spheromak equatorial plane.

Inside the spheromak wall, where the toroidal magnetic field is proportional to (1 / R), for:

**Rc < R < Rs**

the static field energy density is given by:

**Ut = Uto [Ro / R]^2**

Note that **U** is the sum of the static electric field energy density plus the static magnetic field energy density and that for spheromak stability the expressions for **U** inside and outside the spheromak wall must be equal everywhere on the spheromak wall.

Thus at R = Rc, Z = 0:

U = Uo [Ro^2 / ((Ro)^2 + (A Rc)^2)]^2 = Uto [Ro / Rc]^2

and at R = Rs, Z = 0:

U = Uo [Ro^2 / ((Ro)^2 + (A Rs)^2)]^2 = Uto[Ro / Rs]^2

Thus equating the expressions for Uto gives the boundary condition:

[Ro Rc / ((Ro)^2 + (A Rc)^2)]^2 = [Ro Rs / (Ro^2 + (A Rs)^2)]^2

or

[Ro Rc / (Ro^2 + (A Rc)^2)] = [Ro Rs / (Ro^2 + (A Rs)^2)]

or

(Ro^2 + (A Rs)^2) Rc = (Ro^2 + (A Rc)^2) Rs

or

(A Rs)^2) Rc - (A Rc)^2) Rs = (Ro)^2 (Rs - Rc)

or

A^2 Rs Rc (Rs - Rc) = (Ro)^2 (Rs - Rc)

or

**A^2 Rs Rc = Ro^2**

The spheromak shape factor So is defined by:

So^2 = (Rs / Rc)

Note that for **[(A R)^2 + (B Z)^2] >> Ro^2** the dependence of radial electric field from randomly oriented particles on radial distance is the same as for a theoretical point charge.

Spheromaks tend to absorb and emit photons until they reach their stable low energy state.

As shown on other web pages on this web site this spheromak mathematical model accurately predicts the Planck constant and explains the experimentally observed parameters of nuclear magnetic resonance.

**ATOMIC PARTICLE SPHEROMAK:**

The net charge on an atomic particle spheromak is quantized. The mechanism of this net charge quantization is not known. The net charge circulates at the speed of light. The circulating net charge exhibits no inertial mass. The characteristic frequency Fh of an atomic particle spheromak is:

Fh = C / Lh

where:

C = speed of light

and

Lh = charge hose length

= [(Np Lp)^2 + (Nt Lt)^2]^0.5________________

where:

Lt = toroidal turn length

Lp = average toroidal turn length

Np = number of poloidal turns in length Lh

Nt = number of toroidal turns in length Lh

The characteristic frequency Fh of an atomic particle is given by:

**Fh = C / Lh**

Due to spheromak geometry:

Lp = Pi (Rs + Rc)

and

Lt = Pi (Rs - Rc) Kc

and

Ro / (A Rc) = So = A Rs / Ro

where:

Kc = Lt / Pi (Rs - Rc)

Note that Kc is a complex function of [A / B].

**TOTAL ISOLATED SPHEROMAK ENERGY:**

As shown on the web page titled SPHEROMAK ENERGY the total energy of an isolated spheromak is given by:

**Ett = (Ett / Efs) Uo Pi^2 Ro^3 / A^2 B**

where:

Efs = Uo Ro^3 Pi^2 / A^2 B

and

(Ett / Efs) = 0.96 at So^2 = 4.0

**CHARGE HOSE SUMMARY:**

A charge hose is characterized by a net charge **Qs**, an axial current **Ih** and a frequency **Fh**. The net charge gives the particle an external electric field. The net charge current:

**Ih = (Qs C / Lh)**

gives the charged particle an external poloidal magnetic field and an internal toroidal magnetic field. Changing the symmetry axis orientation with respect to an externally applied magnetic field causes the particle to absorb or emit photons. Linear motion of the particle with respect to an external observer gives the particle linear momentum.

**DEFINITIONS:**

Define:

**Nnh** = number of negative charge quanta forming the charge Qs;

**Nph** = number of positive charge quanta forming the charge Qs;

**Lh** = length of current path;

**Vn** = negative charge speed along the current path;

**Vp** = positive charge sped along the current path;

**Qp** = one quantum of positive charge

**Qn** = one quantum of negative charge

**Q** = net charge on a proton

**Qs** = Nnh Qn + Nph Qp

**QUARK THEORY:**

Under the standard model protons are believed to be composed of quarks.

Under quark theory:

Qs = (Qp Nph + Qn Nnh)

For a proton:

Qp = (2 / 3) Q

Nph = 2

Qn = - (1 / 3) Q

Nnh = 1

giving:

(Qp Nph + Qn Nnh) = [(2 Q / 3) (2)] + [(- Q / 3) (1)]

= Q = Qs

**STATIC CHARGE:**

A spheromak must have static charges such that the net static charge for an electron is - Q and the net static charge for a proton is + Q.

If the spheromak static charges conform to quark theory (Standard Model) then for a proton there are two positively charged quarks each with static charge:

+ (2 / 3) Q

and one negatively charged quark with static charge:

(- 1 / 3) Q.

If the spheromak static charges conform to quark theory
(Standard Model) for a neutron then there must be one quark with static charge:

(+ 2 / 3) Q

and two quarks each with static charge:

(- 1 / 3) Q.

In quark theory on decay a neutron emits a -ve portion that forms a free electron and most of the remainder becomes a proton. Note according to quark theory the emission of an electron with a charge of - Q causes a quark with a charge of:

(+ 2 Q / 3)

to change into a quark with a charge of:

(- Q / 3).

**********************************************************************

**DEFINITIONS:**

Nne = number of equivalent electron charges in an atomic nucleus;

Nnp = number of equivalent positron charges in an atomic nucleus;

Nip = number of equivalent proton charges in an atomic nucleus;

Nie = number of equivalent anti-proton charges in an atomic nucleus

Thus:

Number of protons in a nucleus = (Nip - Nne)

Number of neutrons in a nucleus = Nne

**ELECTRON AND POSITRON:**

The total spheromak electromagnetic field energy is the sum of the external electric field energy outside the spheromak wall, the internal electric field energy inside the spheromak wall, the poloidal magnetic field energy outside the spheromak wall and the toroidal magnetic field energy inside the spheromak wall.

The poloidal circulation of charge around a spheromaks main axis of symmetry gives a spheromak its external magnetic moment. Since the toroidal charge motion has two direction possibilities with respect to a particular poloidal magnetic field direction, a spheromak aligned to an external magnetic field has one of two possible states which are of equal energy.

In some materials application of a strong external magnetic field can partially align the electron poloidal magnetic fields causing a phenomena known as Electron Spin Resonance (ESR). ESR has limited general application because in many materials the electron magnetic moments cancel each other.

**PROTON:**

The Standard Model claims that a proton (and other nucleons) are composed of three quarks, two of which each have charge:

**(2 Q / 3)**

and one with charge:

**(- Q / 3)**.

However, all long lived real particles have integral charges, so this assignment of fractional charges to quarks may be just a mathematical construct.

Each proton consists of 3 quarks and the superposition of the three quarks has charge Q.

Note that isolated quarks have never been experimentally observed. However, they exist only as mathematical constructs which explain the existance of known nuclear particles.

The electromagnetic field structure of a proton is believed to be similar to that of an electron but smaller in size.

**ATOMIC PARTICLE DATA:**

Einstein's formula:

**Ett = Mp C^2**

gives the total energy of an isolated proton at rest as:

Ett = 1.67262 X 10^-27 kg X (2.99792458 X 10^8 m / s)^2

= **15.03275887 X 10^-11 J**.

The magnetic moment of a proton is:

1.4106067 X 10^-26 J / T

The Larmor precession frequency for a proton is:

42.57748 MHz / T

Einstein's formula:

**Ett = Me C^2**

gives the total energy of an isolated electron at rest as:

Ett = 9.109383 X 10^-31 kg X (2.99792458 X 10^8 m / s)^2

= **81.87105146 X 10^-15 J**.

The magnetic moment of an electron is:

-928.4763 X 10^-26 J / T

**Pb-207:**

An example of a stable nucleus is a lead-207 where:

**Nip = 2 X 207 = 414**

**Nnp = 207**

and from the atomic number:

**Nne = 207 - 82 = 125**

For Pb-207:

**(Nnp / Nne) = 207 / 125 = 1.656**

It has been experimentally observed that atomic nuclei with:

**(Nnp / Nne) < 1.66**

are unstable and hence are radio active (eg uranium, plutonium, etc).

It has further been experimentally observed that atomic nuclei with:

**(Nnp / Nne) > 2.0**

are likewise radioactive (eg beryllium-7, boron-8, carbon-9,carbon-10, carbon-11, etc.)

There is only a relatively small range of **(Nnp / Nne)** values that result in highly stable atomic nuclei.

**SEMI-STABLE ATOMIC PARTICLE ASSEMBLIES:**

There are about 1000 well documented semi-stable elementary particle assemblies that are known as atomic nuclei. Many of these assemblies are unstable and hence exhibit natural radio activity.

then the nucleus tends to decay by electron emission which decrements

If:

**(Nnp / Nne) > stable value**

and if:

**Nnp < 207**

then the nucleus tends to decay by electron-positron pair production immediately followed by positron emission which together increment **Nne** and hence decrements (Nip - Nne).

If:

**Nnp > 207**

then the nucleus tends to decay by alpha particle (helium-4 nucleus) emission which decrements **Nnp** by 4 and decrements **Nne** by 2, followed by electron emission(s).

Some nuclei are meta-stable energy states that spontaneously absorb or emit small amounts of energy by photon absorption/emission with no change in either **Nnp** or **Nne**.

**NUCLEAR FORCES:**

The above work suggests that so called weak nuclear force is a mathematical construct resulting from variable neutron decay associated with proton proximity while strong nuclear forces are the result of overlapping electric and magnetic fields between adjacent spheromaks.

This web page last updated April 15, 2021.

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