Draft:Original research/Radiation physics

Radiation physics is the laboratory physics concerned with radiation both natural and experimentally or commercially generated.

Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space.

Def. an action or process of throwing or sending out a traveling ray in a line, beam, or stream of small cross section is called radiation.

The term radiation is often used to refer to the ray itself.

Def. “[t]he shooting forth of anything from a point or surface, like the diverging rays of light; as, the radiation of heat” is called radiation.

Rays may have a temporal, spectral, or spatial distribution.

They may also be dependent on other variables as yet unknown.

Particle radiation consists of a stream of charged or neutral particles, from the size of subatomic elementary particles upwards of rocky, liquid, plasma, and gaseous objects to even larger more loosely bound entities such as galaxies, galaxy clusters and strings with measurable motion.

Physics
Physics is a "science that deals with matter and energy and their interactions", forces (weak and strong nuclear) and fields such as gravity, electric, and magnetic.

Laboratory
Def. "a room, building or institution equipped for scientific research, experimentation or analysis" is called a laboratory.

Safety
Def. the "condition or feeling of being safe" is called safety.

Def.

is called safe.
 * 1) not "in danger; free from harm's reach",
 * 2) free "from risk; harmless; riskless",
 * 3) providing "protection from danger; providing shelter", or
 * 4) not "in danger from the specified source of harm"

Practical Safety can be defined as "anything done to prevent accidents or reduce their effects". It is generally a subject with much unnecessary confusion. Essentially, safety breaks down into 2 major categories:

Safety Technology: engineering solutions designed to eliminate / reduce hazards.

Safety Behaviour: defined safe actions using in conjunction with safety technology.

Theoretical radiation physics
Def. the "study of the effects of ionizing radiation on matter, and of its measurement" is called radiation physics.

Electromagnetics
The Larmor radius is the radius of the circular motion of a charged particle] in the presence of a uniform magnetic field.

“[F]or a particle of energy E in EeV and charge Z in a magnetic field B in µG [the Larmor radius (RL)] is roughly”


 * $$R_L = 1 kpc \frac{E}{Z B}$$

where
 * $$R_L \ $$ is the Larmor radius,
 * $$E\ $$ is the energy of the particle in EeV
 * $$Z \ $$ is the charge of the particle, and
 * $$B \ $$ is the constant magnetic field.

Neutrons
"The nuclear processes that produce cosmogenic 36Cl in rocks are spallation, neutron capture, and muon capture. The first two processes dominate production on the land surface; muon production in Ca and K becomes more important with increasing depth (Rama and Honda, 1961)."

"The decay of radioactive U and Th also give rise to the production of 36Cl, via neutron capture (Bentley et al., 1986)."

"The production rate of cosmogenic 36Cl in bedrock and regolith exposed at Earth's surface is dependent on its calcium, potassium, and chloride content and can be expressed by the equation


 * $$P = \psi_{Ca}(C_{Ca}) + \psi_K(C_K) + \psi_n(\sigma_{35}N_{35}/\Sigma \sigma_iN_i),$$

where $$\psi_K$$ and $$\psi_{Ca}$$ are the total production rates (including production due to slow negative muons) of 36Cl due to potassium and calcium, respectively; $$C_K$$ and $$C_{Ca}$$ are the elemental concentrations of potassium and calcium, respectively; and $$\psi_n$$ is the thermal neutron capture rate, which is dependent on the fraction of neutrons stopped by 35Cl $$(\sigma_{35} N_{35}/\Sigma \sigma_i N_i),$$ as determined by the effective cross sections of 35Cl$$(\sigma_{35})$$ and all other absorbing elements $$(\Sigma \sigma)$$ and their respective abundances $$(N_{35}$$ and $$N_i)$$."

Protons
Rutherford backscattering spectrometry (RBS) is an analytical technique sometimes referred to as high-energy ion scattering (HEIS) spectrometry. RBS is used to determine the structure and composition of materials by measuring the backscattering of a beam of high energy protons or ions impinging on a piece of material such as a dust grain.

If the energy of the incident proton is increased sufficiently, the Coulomb barrier is exceeded and the wavefunctions of the incident and struck particles overlap. This may result in nuclear reactions in certain cases, but frequently the interaction remains elastic, although the scattering cross-sections may fluctuate wildly as a function of energy. This case is known as "Elastic (non-Rutherford) Backscattering Spectrometry" (EBS).

We can describe Rutherford backscattering as an elastic (hard-sphere) collision between a high kinetic energy proton from the incident beam (the projectile) and a stationary particle located in the dust grain (the target). Elastic in this context means that no energy is either lost or gained during the collision.

In some circumstances a collision may result in a nuclear reaction, with the release of considerable energy. Nuclear reaction analysis (NRA) is very useful for detecting light elements.

The energy E1 of the scattered projectile is reduced from the initial energy E0:


 * $$E_1 = k \cdot E_0, $$

where k is known as the kinematical factor, and


 * $$k = \left(\frac{m_1 \cos{\theta_1} \pm \sqrt{m_2^2 - m_1^2(\sin{\theta_1})^2}}{m_1 + m_2}\right)^2,$$

where particle 1 is the projectile, particle 2 is the target nucleus, and $$\theta_1$$ is the scattering angle of the projectile in the laboratory frame of reference (that is, relative to the observer). The plus sign is taken when the mass of the projectile is less than that of the target, otherwise the minus sign is taken.

To describe the probability of observing such an event. For that we need the differential cross-section of the backscattering event:


 * $$\frac{d\omega}{d\Omega} = \left(\frac{Z_1Z_2e^2}{4E_0}\right)^2

\frac{1}{\left(\sin{\theta/2}\right)^4},$$

where $$Z_1$$ and $$Z_2$$ are the atomic numbers of the incident proton and target nucleus. From the centre of mass frame of reference and is therefore not a function of the mass of either the projectile or the target nucleus.

The scattering angle $$\theta_1$$ is not the same as the scattering angle $$\theta$$ (although for RBS experiments they are usually very similar).

A scattering cross-section is zero implies that the projectile never comes close to the target, nor penetrates the electron cloud surrounding the nucleus. The pure Coulomb formula for the scattering cross-section shown above must be corrected for this screening effect, which becomes more important as the energy of the projectile decreases.

While large-angle scattering only occurs for protons which scatter off target nuclei, inelastic small-angle scattering can also occur off the sample electrons. This results in a gradual decrease in protons which penetrate more deeply into the sample, so that backscattering off interior nuclei occurs with a lower "effective" incident energy. The amount by which the ion energy is lowered after passing through a given distance is referred to as the stopping power of the material and is dependent on the electron distribution. This energy loss varies continuously with respect to distance traversed, so that stopping power is expressed as


 * $$S(E) = -{dE \over dx}. $$

For high energy protons stopping power is usually proportional to $$\frac{Z_2}{E}$$.

Stopping power or, stopping force has units of energy per unit length. It is generally given in thin film units, that is eV /(atom/cm2) since it is measured experimentally on thin films whose thickness is always measured absolutely as mass per unit area, avoiding the problem of determining the density of the material which may vary as a function of thickness. Stopping power is now known for all materials at around 2%, see http://www.srim.org.

When a beam of protons with parallel trajectories is incident on a target atom, scattering off that atom prevents or blocks collisions in a cone-shaped region "behind" the target relative to the beam. This occurs because the repulsive potential of the target atom bends close ion trajectories away from their original path. The radius of this blocked region, at a distance L from the original atom, is given by


 * $$R = 2\sqrt{\frac{Z_1Z_2e^2L}{E_0}}$$

When a proton is scattered from deep inside a sample, it can then re-scatter off a second atom, creating a second blocked cone in the direction of the scattered trajectory. This can be detected by carefully varying the detection angle relative to the incident angle.

Channeling is observed when the incident beam is aligned with a major symmetry axis of the crystal. Incident protons which avoid collisions with surface atoms are excluded from collisions with all atoms deeper in the sample, due to blocking by the first layer of atoms. When the interatomic distance is large compared to the radius of the blocked cone, the incident protons can penetrate many times the interatomic distance without being backscattered. This can result in a drastic reduction of the observed backscattered signal when the incident beam is oriented along one of the symmetry directions, allowing determination of a sample's regular crystal structure. Channeling works best for very small blocking radii, i.e. for protons.

The tolerance for the deviation of the proton beam angle of incidence relative to the symmetry direction depends on the blocking radius, making the allowable deviation angle proportional to


 * $$\sqrt{\frac{Z_1Z_2}{E_0d}}$$

While the intensity of an RBS peak is observed to decrease across most of its width when the beam is channeled, a narrow peak at the high-energy end of a larger peak will often be observed, representing surface scattering from the first layer of atoms. The presence of this peak opens the possibility of surface sensitivity for RBS measurements.

Beta particles
Def. "the non-linear scattering of radiation off electrons" is called induced Compton scattering.

"The effect of scattering is to move photons to lower frequencies." "[T]he fact that the radio pulses [from a pulsar] are not suppressed by induced scattering suggests that the wind's Lorentz factor exceeds ~104.

The Lorentz factor is defined as:


 * $$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}} = \frac{1}{\sqrt{1 - \beta^2}} = \frac{\mathrm{d}t}{\mathrm{d}\tau} $$

where:


 * v is the relative velocity between inertial reference frames,
 * &beta; is the ratio of v to the speed of light c.
 * &tau; is the proper time for an observer (measuring time intervals in the observer's own frame),
 * c is the speed of light.

As an example, "[t]he power into the Crab Nebula is apparently supplied by an outflow [wind] of ~1038 erg/s from the pulsar" where there are "electrons (and positrons) in such a wind". These beta particles coming out of the pulsar are moving very close to light speed.

Electrons
Def. “[a] measure of the number of electrons per unit volume of space” is called an electron density.

Electron density is the measure of the probability of an electron being present at a specific location. In molecules, regions of electron density are usually found around the atom, and its bonds.

In quantum chemical calculations, the electron density, ρ(r), is a function of the coordinates r, defined so ρ(r)dr is the number of electrons in a small volume dr. For closed-shell molecules, $$ \rho(\mathbf{r}) $$ can be written in terms of a sum of products of basis functions, φ:


 * $$ \rho(\mathbf{r}) = \sum_\mu \sum_\nu P_{\mu \nu} \phi_\mu(\mathbf{r}) \phi_\nu(\mathbf{r}) $$

where P is the density matrix. Electron densities are often rendered in terms of an isosurface (an isodensity surface) with the size and shape of the surface determined by the value of the density chosen, or in terms of a percentage of total electrons enclosed.

Positrons
Def. "[a]n exotic atom consisting of a positron and an electron, but having no nucleus" or "[a]n onium consisting of a positron (anti-electron) and an electron, as a particle–anti-particle bound pair" is called positronium.

Being unstable, the two particles annihilate each other to produce two gamma ray photons after an average lifetime of 125 ps or three gamma ray photons after 142 ns in vacuum, depending on the relative spin states of the positron and electron.

The singlet state with antiparallel spins ([spin quantum number] S = 0, Ms = 0) is known as para-positronium (p-Ps) and denoted. It has a mean lifetime of 125 picoseconds and decays preferentially into two gamma quanta with energy of 511 keV each (in the center of mass frame). Detection of these photons allows for the reconstruction of the vertex of the decay. Para-positronium can decay into any even number of photons (2, 4, 6, ...), but the probability quickly decreases as the number increases: the branching ratio for decay into 4 photons is $1.439$.

para-positronium lifetime (S = 0):
 * $$t_{0} = \frac{2 \hbar}{m_e c^2 \alpha^5} = 1.244 \times 10^{-10} \; \text{s}$$

The triplet state with parallel spins (S = 1, Ms = −1, 0, 1) is known as ortho-positronium (o-Ps) and denoted 3S1. The triplet state in vacuum has a mean lifetime of $142.05 ns$ and the leading mode of decay is three gamma quanta. Other modes of decay are negligible; for instance, the five photons mode has branching ratio of ~$1$.

ortho-positronium lifetime (S = 1):
 * $$t_{1} = \frac{\frac{1}{2} 9 h}{2 m_e c^2 \alpha^6 (\pi^2 - 9)} = 1.386 \times 10^{-7} \; \text{s}$$

Blues
The image above shows a blue glow in the surrounding air from emitted cyclotron particulate radiation.

At left is an image that shows the blue glow resulting from a beam of relativistic electrons as they slow down. This deceleration produces synchrotron light out of the beam line of the National Synchrotron Light Source.

Plasma cleaning at the right involves the removal of impurities and contaminants from surfaces through the use of an energetic plasma created from gaseous species. Gases such as argon and oxygen, as well as mixtures such as air and hydrogen/nitrogen are used. The plasma is created by using high frequency voltages (typically kHz to >MHz) to ionise the low pressure gas (typically around 1/1000 atmospheric pressure), although atmospheric pressure plasmas are now also common.

Cyans
Cyan light has a wavelength of between 490 and 520 nanometers, between the wavelengths of blue and green.

Planck's [equation] describes the amount of [spectral radiance at] a certain wavelength radiated by a black body in thermal equilibrium.

In terms of wavelength (λ), Planck's equation is written: as
 * $$B_\lambda(T) =\frac{2 hc^2}{\lambda^5}\frac{1}{ e^{\frac{hc}{\lambda k_\mathrm{B}T}} - 1}$$

where B is the spectral radiance, T is the absolute temperature of the black body, kB is the Boltzmann constant, h is the Planck constant, and c is the speed of light.

This form of the equation contains several constants that are usually not subject to variation with wavelength. These are h, c, and kB. They may be represented by simple coefficients: c1 = 2h c2 and c2 = h c/kB.

By setting the first partial derivative of Planck's equation in wavelength form equal to zero, iterative calculations may be used to find pairs of (λ,T) that to some significant digits represent the peak wavelength for a given temperature and vice versa.


 * $$\frac{\partial B}{\partial \lambda} = \frac{c1}{\lambda^6}\frac{1}{ e^{\frac{c2}{\lambda T}} - 1}[\frac{c2}{\lambda T}\frac{1}{ e^{\frac{c2}{\lambda T}} - 1}e^{\frac{c2}{\lambda T}} - 5] = 0.$$

Or,


 * $$\frac{c2}{\lambda T}\frac{1}{ e^{\frac{c2}{\lambda T}} - 1}e^{\frac{c2}{\lambda T}} - 5 = 0.$$


 * $$\frac{c2}{\lambda T}\frac{1}{ e^{\frac{c2}{\lambda T}} - 1}e^{\frac{c2}{\lambda T}} = 5.$$

Use c2 = 1.438833 cm K.

For a star to have a peak in the cyan, iterative calculations using the last equation yield the pairs: approximately (476 nm, 6300 K) and (495 nm, 6100 K).

Although Planck's equation is not an exact fit to a star's spectral radiance, it may be close enough to suggest if a star is an astronomical cyan source.

Superluminals
"The existence of superluminal energy transfer has not been established so far, and one may ask why. There is the possibility that superluminal quanta just do not exist, the vacuum speed of light being the definitive upper bound. There is another explanation, the interaction of superluminal radiation with matter is very small, the quotient of tachyonic and electric fine-structure constants being q2/e2 ≈ 1.4 x 10-11 [5], and therefore superluminal quanta are hard to detect."

At right is an example of Cherenkov radiation. Cherenkov radiation (also spelled Čerenkov) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium. Cherenkov radiation is an example of medium specific superluminals.

Plasma objects
In spacecraft propulsion, a Hall thruster is a type of ion thruster in which the propellant is accelerated by an electric field. Hall thrusters trap electrons in a magnetic field and then use the electrons to ionize propellant, efficiently accelerate the ions to produce thrust, and neutralize the ions in the plume. Hall thrusters are sometimes referred to as Hall effect thrusters or Hall current thrusters. Hall thrusters are often regarded as a moderate specific impulse (1,600 s) space propulsion technology. Hall thrusters operate on a variety of propellants, the most common being xenon. Other propellants of interest include krypton, argon, bismuth, iodine, magnesium, and zinc.

Moon
"The nearside, with its sea of dark gray basins standing in contrast to the brilliant white powder that covers the rest of its face, varies dramatically from the farside, which is marked with countless smaller craters in a more uniform distribution."

The theory: "Earth’s Moon was struck by a tiny dwarf planet long ago".

"Using computer models to simulate what may have happened to the Moon’s surface long ago, researchers suggest the most likely scenario seems to be the collision between the Moon and a very large body. The impact of a dwarf planet as large as 480 miles across would have struck what we see today as the Moon’s nearside at a speed of 14,000 miles per hour."

"The two-moon theory suggests that Earth’s moon duo may have at one point collided and merged, leaving the Moon as we see it today looking oddly unsymmetrical."

"The dwarf planet collision scenario assumes that whatever the body that struck the Moon was, it was in its own path around the Sun and just happened to be in the right place at the right time to strike Earth’s natural satellite. This [...] would also explain why the crust on the farside of the Moon is different than that of its nearside."

"We demonstrate that a large body slowly impacting the nearside of the Moon can reproduce the observed crustal thickness asymmetry and form both the farside highlands and the nearside lowlands. Additionally, the model shows that the resulting impact ejecta would cover the primordial anorthositic crust to form a two‐layer crust on the farside, as observed."

Mathematics
The Sakuma–Hattori equation is a mathematical model for predicting the amount of thermal radiation, radiometric flux or radiometric power emitted from a perfect blackbody or received by a thermal radiation detector.

In its general form it looks like:
 * $$S(T) = \frac{C}{\exp\left(\frac{c_2}{\lambda _x T}\right)-1}$$

where:

The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation.

The relationship of the Stokes parameters to intensity and polarization ellipse parameters is shown in the equations below and the figure at right.


 * $$ \begin{align}

S_0 &= I \\ S_1 &= p I \cos 2\psi \cos 2\chi\\ S_2 &= p I \sin 2\psi \cos 2\chi\\ S_3 &= p I \sin 2\chi. \end{align} $$

Here $$p I$$, $$2\psi$$ and $$2\chi$$ are the spherical coordinates of the three-dimensional vector of cartesian coordinates$$(S_1, S_2, S_3)$$. $$I$$ is the total intensity of the beam, and $$p$$ is the degree of polarization. The factor of two before $$\psi$$ represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°, while the factor of two before $$\chi$$ indicates that an ellipse is indistinguishable from one with the semi-axis lengths swapped accompanied by a 90° rotation. The four Stokes parameters are sometimes denoted I, Q, U and V, respectively.

If given the Stokes parameters one can solve for the spherical coordinates with the following equations:


 * $$ \begin{align}

I &= S_0 \\ p &= \frac{\sqrt{S_1^2 + S_2^2 + S_3^2}}{S_0} \\ 2\psi &= \mathrm{atan} \frac{S_2}{S_1}\\ 2\chi &= \mathrm{atan} \frac{S_3}{\sqrt{S_1^2+S_2^2}}.\\ \end{align}$$

Sciences
A particle on the exact design trajectory (or design orbit) of the accelerator only experiences dipole field components, while particles with transverse position deviation $$\scriptstyle x(s)$$ are re-focused to the design orbit. For preliminary calculations, neglecting all fields components higher than quadrupolar, an inhomogenic Hill differential equation


 * $$ \frac{d^2}{ds^2}\,x(s) + k(s)\,x(s) = \frac{1}{R} \, \frac{\Delta p}{p} $$

can be used as an approximation, with
 * a non-constant focusing force $$\scriptstyle k(s)$$, including strong focusing and weak focusing effects
 * the relative deviation from the design beam impulse $$\scriptstyle \Delta p / p$$
 * the trajectory curvature radius $$\scriptstyle R$$, and
 * the design path length $$\scriptstyle s$$,

thus identifying the system as a parametric oscillator. Beam parameters for the accelerator can then be calculated using ray transfer matrix analysis; e.g., a quadrupolar field is analogous to a lens in geometrical optics, having similar properties regarding beam focusing (but obeying Earnshaw's theorem).

Cyclotrons
A cyclotron is a compact type of particle accelerator in which charged particles in a static magnetic field are travelling outwards from the center along a spiral path and get accelerated by radio frequency electromagnetic fields. Cyclotrons accelerate charged particle beams using a high frequency alternating voltage which is applied between two "D"-shaped electrodes (also called "dees"). An additional static magnetic field $$B$$ is applied in perpendicular direction to the electrode plane, enabling particles to re-encounter the accelerating voltage many times at the same phase. To achieve this, the voltage frequency must match the particle's cyclotron resonance frequency


 * $$f = \frac{q B}{2\pi m}$$,

with the relativistic mass m and its charge q. This frequency is given by equality of centripetal force and magnetic Lorentz force. The particles, injected near the center of the magnetic field, increase their kinetic energy only when recirculating through the gap between the electrodes; thus they travel outwards along a spiral path.

Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that causes them to emit radiation (and to spiral around the magnetic field lines). Cyclotron radiation is emitted by all charged particles travelling through magnetic fields, however, not just those in cyclotrons. Cyclotron radiation from plasma in the interstellar medium or around black holes and other astronomical phenomena is an important source of information about distant magnetic fields. The power (energy per unit time) of the emission of each electron can be calculated using:

$${-dE \over dt}={\sigma_t B^2 V^2 \over c \mu_o} $$

where E is energy, t is time, $$ \sigma_t $$ is the Thomson cross section (total, not differential), B is the magnetic field strength, V is the velocity perpendicular to the magnetic field, c is the speed of light and $$ \mu_o $$ is the permeability of free space.

"Electron beams can be generated by thermionic emission, field emission or the anodic arc method. The generated electron beam is accelerated to a high kinetic energy and focused towards the [target]. When the accelerating voltage is between 20 kV – 25 kV and the beam current is a few amperes, 85% of the kinetic energy of the electrons is converted into thermal energy as the beam bombards the surface of the [target]. The surface temperature of the [target] increases resulting in the formation of a liquid melt. Although some of incident electron energy is lost in the excitation of X-rays and secondary emission, the [target] material evaporates under vacuum."

Hypotheses

 * 1) Radiation physics designs radiation detectors for human safety.