# Multiphoton momentum trasfer

• 1Keenan
In summary, the book discusses the ejection of an electron from a focused laser beam and states that the kinetic energy of the electron is given by the formula ΔU=(γ-1)mc², where γ is the Lorentz factor and mc² is the total energy of a relativistic massive particle. The energy is extracted from the electromagnetic field through multiphoton momentum transfer. However, the book does not provide a demonstration of this formula. It is simply a consideration of energy conservation and does not explain the mechanism of how the energy is extracted from the electromagnetic field. The concept of multiphoton can be confusing in this context.

#### 1Keenan

Hi everybody,

I'm reading P. Gibbon book "Short Pulse Laser Interaction with Matters", and I'm having a problem.
Describing the ejection of an electron from a focused laser beam the book says, on pag 39, that "the kinetic energy of the electron is given by:

$\Delta$U=($\gamma$-1)mc$^{2}$

This energy is extracted from electromagnetic field via multiphoton momentum transfer."

I would like to know the demostration of that formula, since no clue is given in the book.

Thanks for helping

ɣmc² is the total energy of a relativistic massive particle. When you subtract the rest energy mc² from this, you get the relativistic kinetic energy.

This is just an energy conservation consideration and has nothing to do with the concrete mechanism of how this energy is extracted from the em field.

I get confused because of the multiphoton stuff...

Thank you very much

## 1. What is multiphoton momentum transfer?

Multiphoton momentum transfer is a phenomenon in which the momentum of an object is changed by the absorption of multiple photons. This can occur when an object is exposed to a high-intensity laser beam, where multiple photons are absorbed simultaneously, resulting in a transfer of momentum to the object.

## 2. How does multiphoton momentum transfer differ from single photon momentum transfer?

In single photon momentum transfer, only one photon is absorbed by an object, resulting in a relatively small change in momentum. In multiphoton momentum transfer, the absorption of multiple photons leads to a much larger change in momentum.

## 3. What are some applications of multiphoton momentum transfer?

Multiphoton momentum transfer has various applications in fields such as laser technology, materials science, and biophysics. It can be used to manipulate and control the movement of microscopic particles, as well as to study the properties of materials and molecules.

## 4. Can multiphoton momentum transfer be used for propulsion?

Yes, multiphoton momentum transfer has been studied as a potential method for spacecraft propulsion. By using high-intensity laser beams to transfer momentum, spacecraft could potentially achieve high speeds without the need for traditional propellants.

## 5. Are there any limitations or challenges in studying multiphoton momentum transfer?

One limitation of studying multiphoton momentum transfer is the high level of precision required in experimental setups. The intensity and focus of the laser beam must be carefully controlled to achieve the desired results. Additionally, the nonlinear nature of this phenomenon can make it difficult to predict and model accurately.