Microwave radiation is termed non-ionizing because a microwave photon does not have enough energy to extract an electron and cause ionization. However, upon certain conditions microwaves can mediate hydrogen ionization and in general Rydberg atom ionization.
Note: A Rydberg atom is an excited atom with one or more electrons at a very high shell i.e. an orbital with a very high principal quantum number n located very far from the nucleus. The existence of these atoms was demonstrated first for hydrogen. Rydberg atoms form commonly in plasmas due to the recombination of electrons and positive ions. There are different techniques that can create Rydberg atoms such as electron beams i.e. electron impact excitation, as well as optical excitation. (Reference: https://en.wikipedia.org/wiki/Rydberg_atom). While for ground state (non-excited) hydrogen the n is 1, it is possible to create a hydrogen Rydberg atom with n=60, n=70 etc.
Microwave ionization of hydrogen requires absorption of approximately 70 photons (multiphoton process) and can be explained as the result of the appearance of chaotic motion of the electron due. Due to this, the electron is said to diffuse over increasing energy levels (diffusive energy excitation) until it reaches the ionization continuum and is thus ionized.
Note: The continuum represents a group of energy levels whose gaps are negligibly small and whose energy corresponds to the state where the electron’s kinetic energy surpasses the potential energy that keeps it bound by the atom.
In standard conditions, the electron energy E only performs small oscillations around its initial value and this does not allow ionization. Rydberg atoms subjected to a linearly polarized microwave field of frequency ω and amplitude F are described by a Hamiltonian which explicitly depends on time. Once amplitude F exceeds a threshold value which generally depends on ω, the classical electron may exhibit chaotic motion, absorb energy from the driving field, and diffuse over increasing values of the classical action variable until it reaches the continuum and is thus ionized (ref.).
A special quantal energy transport occurs with a certain diffusion constant, as a result of which under chaotic classical dynamics, a diffusive broadening of the population distribution over the bound states of the real atom occurs (ref.).
Note: The energy of the electron increases in a diffusive way, with a certain diffusion rate. This leads to ionization of the electron after a typical diffusive time scale. Such classical diffusive ionization requires many microwave periods and quantum interference effects can suppress it leading to quantum localization of chaos.
For a given n and a given frequency ω, at a certain E field, the motion of the hydrogen Rydberg atom becomes chaotic and it is then free to diffuse towards the ionization continuum. The critical field is determined based on resonance overlap in phase space. The Chirikov resonance overlap analysis is applied which leads to a pendulum Hamiltonian. It is concluded that any sinusoidally-driven, one dimensional system can be approximated by a pendulum system near a weakly-perturbed resonance. The Chirikov resonance overlap criterion states that the onset of chaos should occur when neighboring resonances overlap. We can determine conditions for resonance and for actions resonant with subharmonics of the applied frequency.
Classical theory provides the following explanation of the ionization process: resonance overlap leads to chaotic electron trajectories and the energy of a chaotically meandering electron grows in a diffusive-like fashion, resulting in ionization. The onset of chaos results in ionization.
Also a second driving frequency tends to increase the degree of ionization.
There is also the argument that classical resonance overlap (leading to classical chaos) is equivalent in quantum mechanics terms in a strong level mixing by the field resulting in the state vector spreading to include the continuum. This is analogous to classical chaotic trajectories meandering into the continuum.
In quantum mechanics, the hydrogen atom is discussed typically in spherical coordinates. The hydrogen states are determined by the principal quantum number n, the angular quantum number l, the magnetic quantum number m and also the spin quantum number s which is omitted here. When we refer to the microwave fields used in the ionization of Rydberg atoms, we tend to use parabolic coordinates. In parabolic coordinates the hydrogen states are known as Stark states and are classified by the parabolic quantum numbers n1 and n2 and the mangetic quantum number m.
A pioneering experiment by Bayfield and Koch in 1974 demonstrated that a microwave field can induce ionization of highly excited hydrogen and Rydberg atoms. The scientists showed that a hydrogen atom with a principal quantum number of n=66 (produced by charge exchange excitation) could be ionized by a microwave of 9.9 GHz and a strength above a critical value of 20 volts/cm. It is noted that since the transition from n=66 to n=67 has a Bohr resonance frequency of 22 GHz, the applied frequency field is only 40% of the resonance frequency.
The energy of ionization was determined to be approximately 70 times greater than the energy of the microwave photon, which would be suggestive of the fact that 70 photons are required for the ionization. This would indicate that this is a multiphoton process. It was also demonstrated that the strength/intensity or the total energy of the field was important and not its frequency i.e. its detailed time variation. This dependence is attributed to chaotic behavior, which makes available a large number of phase space in a diffusive manner. This is known as stochastic excitation. It is believed that microwave ionization may be operating in astrophysical locations. It is noted that ionization refers to the sum of "true ionization" and excitation to bound states above a certain cut-off limit. Experiments show the absorption of a large number of photons from a field comparable in strength to the Coulomb field.
References:
Chaotic enhancement in microwave ionization of Rydberg atoms http://www.quantware.ups-tlse.fr/dima/myrefs/my098.pdf
Microwave ionization of hydrogen atoms http://www.scholarpedia.org/article/Microwave_ionization_of_hydrogen_atoms
Astrophysical Plasmas and Fluids, by Vinod Krishan http://bit.ly/39FbbX3
Chaos in Atomic Physics, by R. Blümel, W. P. Reinhardt http://bit.ly/38LECqg
Progress in Optics http://bit.ly/38CD5mG
Mosaic http://bit.ly/38vqEZE
"Counting the electrons in a multiphoton ionization by elastic scattering of microwaves" https://www.nature.com/articles/s41598-018-21234-y
"Chaotic enhancement in microwave ionization of Rydberg atoms" http://www.quantware.ups-tlse.fr/dima/myrefs/my098.pdf
"Forced field ionization of Rydberg states for the production of monochromatic beams" http://www.physics.purdue.edu/~robichf/papers/pra95.043409.pdf
"Order and chaos in strong fields" https://www.nature.com/articles/336518a0.pdf?platform=hootsuite
"Diffusive Photoelectric Effect in Hydrogen Atom http://www.quantware.ups-tlse.fr/dima/adr1/node22.html
"From coherent to noise-induced microwave ionization of Rydberg atoms" https://www.researchgate.net/publication/13377309_From_coherent_to_noise-induced_microwave_ionization_of_Rydberg_atoms
"Addition of weak broadband microwave noise enhances the ionization".
"Near-classical noise enhancement of microwave ionization of Rydberg atoms."
https://www.ncbi.nlm.nih.gov/pubmed/12779902
"The ionization of the highly excited hydrogen atom in a strong external microwave field is a classically chaotic, near-classical quantum system for microwave frequencies somewhat below the initial Kepler electron orbit frequency. The addition of microwave noise is found to reduce the sinewave microwave field needed for ionization, modifying the near-classical fast process responsible for the microwave energy absorption. A classical numerical calculation based upon a many-frequency model of the noise qualitatively reproduces the observed noise enhancement."
https://aip.scitation.org/doi/abs/10.1063/1.1722222
"Modulation of the electron average energy at twice the frequency of the applied field becomes important at either high pressure or low frequency and modifies the values of the breakdown field."
https://etd.lib.metu.edu.tr/upload/12612910/index.pdf
"Any gas medium contains free ions and free electrons which arise from interactions between cosmic rays, environmental radiation with the gas atoms or a result of field emission from any violence on the surface, where electric fields are strong [3, 5]. These free charge carriers are accelerated through these electric field lines and they start to collide with the atoms or molecules, encountered with these free charge carriers [3]."
"This avalanche effect is caused by the new produced electrons and ions. An electron multiplication process takes place."
Note: This may be releant to the MASER effect.