Enhancement of Electron Temperature under Dense Homogenous Plasma by Pulsed Laser Beam

The applications of hot plasma are many and numerous applications require high values of the temperature of the electrons within the plasma region. Improving electron temperature values is one of the important processes for using this specification in plasma for being adopted in several modern applications such as nuclear fusion, plating operations and in industrial applications. In this work, theoretical computations were performed to enhance electron temperature under dense homogeneous plasma. The effect of power and duration time of pulsed Nd:YAG laser was studied on the heating of plasmas by inverse bremsstrahlung for several values for the electron density ratio. There results for these calculations showed that the effect of increasing the values of the laser pulse power (25-250kW) led to decrease the absorption coefficient values by 58.3% and increase the electron temperature by 50.0% at duration pulse time 0.5ns and electron density ratio 0.1. Furthermore, the ratio of electron density increasing and pulse duration time led to increase the higher values of the electron temperature. The results of the calculations showed the effect of the laser power, the percentage of electron density, and the pulse duration for improving the electron temperature. It is possible to control the temperature of the electrons with one of the plasma parameters or the laser beam used, and that it gives a clear indication of researchers in this field to choose the optimal wavelength of the laser beam and electron density ratios for the plasma.


Introduction:
Electron temperature is the primary measurement of the kinetic energy of electrons inside plasma. The electron temperature is an important parameter in determining the classification of the plasma (thermal and non thermal) by comparing its values with the temperature of the ions inside the plasma. Therefore, the researchers focused on this parameter in order to change the values of electron temperature according to the requirements of practical applications such as including nuclear fusion, plating operations and in industrial applications (1,2,3).There are several methods for heating plasma and varying the electron temperature values such as, applying a magnetic field or interacting by a laser beam with plasma (4,5,6,7).The process of energy absorbing of the laser beam occurs by inverse bremsstrahlung (IB).
The (IB) process refers to absorb the energy of the photons by plasma electrons and gaining energy leads to heating the plasma and raising the temperature of the electrons. These are carried out with two techniques collisionless and collisional process.
In collisionless technology, the free electrons are absorbed of the photon's energy directly while in collisional technology, the energy of the electrons will be transferred to the neutral ions and atoms by colliding (8,9).
In this work, theoretical computations were done by solving equations for the interaction of the laser beam pulse with the plasma region to study the parameters affecting for the absorption coefficient of the laser beam energy and plasma heating in (IB) method. In this propose model, the homogenous plasma heating phenomenon using inverse bremsstrahlung absorption was studied by using pulsed neodymium laser beam with Gaussian distribution shape . The type of the interaction( under dense or over dense plasma) can be determined according to the values of critical density of plasma (n c ) and unitless laser amplitude(a o ) as the following ( Where λ and I are the wavelength and intensity of laser pulse respectively. So, the case of under dense plasma type is achieved when n c > n e or ω L > ω p where n e is the plasma electron density, ω L is the angular frequency of laser beam and ω p is the plasma frequency. Also, the over dense plasma type is achieved at the reverse of these conditions. On the other hand, the value of a o is used for distinguishing the type of interaction region (nonrelativistic at a o <1 and relativistic at a o >1). The research includes the study of the parameters affecting the heated homogenous plasma using inverse bremsstrahlung absorption (IB) interaction pulsed laser beam with plasma. Furthermore, the Gaussian shape is assumed for pulses temporal laser beam tacks a form (12) Where P max is a peak power of laser pulse, t is time step and τ p is full width at half for laser pulse duration. In the case of liner (IB), the absorption coefficient α(T e ) in m -1 is given by (13 ) Where the ratio electron density n o = n e /n c , T e is temperature of electron in ( eV) , k B is Boltazmaan constant, Z is ion charge and   e T g is the average gaunt factor in hydrodynamic approach (the quantum effect is ignored ) given by (14)  Where m e is electron mass, ν is laser beam frequency and γ g is a constant called Euler-Mascheroni = 1.781 (14). The energy absorbed by the electrons in plasma from the laser beam per unit length Q A (t) is given by eq.(6) The amount of increases in the electron temperature Te (add) (t) is calculated from the equation where A= π r 2 is the area of laser beam with a radius r. So ,it can be calculated the new values of electron temperature T e (new) (t)

Results and Discussion:
The proposed model included a pulsed Nd:YAG laser at wavelength λ =1.06 μm and radius beam 100 µm interacting with homogenous plasma at initial electron temperature T e = 3 eV and Z=1. According to eq.1, the critical density n c = 9.7899x10 20 cm -3 , and using the range of the electron density ratio n o (0.1-0.7), so n c > n e and the case was under dense as mentioned. The computations were done with the aid of equations 1 to 8 to study the effective parameters for heating a plasma region by a pulsed laser beam as the following:

Laser pulse profiles
The research adopted the Gaussian profile of the Nd:YAG laser pulse with a wavelength 1.06 µm ,which interacted with the plasma region. It takes the form in eq.3, and for five values of peak power laser beam (25, 75,125,175and250kW) as shown in Fig.1.

Absorption of pulsed laser
The effect of changing the maximum power of the pulsed Nd:YAG laser with the plasma on the inverse bremsstrahlung absorption coefficient was studied as in Fig.2. The absorption coefficient values decreased with increasing laser beam power. The reason for this behavior is that in collisional absorption method, as increasing the beam power the laser beam will spread and propagated through the plasma without transferring its energy to the electrons, thus the absorption coefficient will decrease(6).

467:
Heating under dense plasma by laser pulse The inverse bremsstrahlung absorption of the laser beam in under dense plasma region and the effective parameters on the values of plasma electron temperature at initial value 3eV were studied as the following: Peak power of the laser beam The effect of the peak values power of the pulsed Nd:YAG laser on the electron temperature in the plasma with n o = 0.1 and the time for duration pulse 5x10 -10 sec were calculated as shown in Fig.  4 It is clear from the figure that the enhancement of electron temperature values was achieved with increasing the peak power of the pulsed laser beam. The decrease in the absorption coefficient values as in Fig 2 led to an increase in the electron temperature values, which was the same behavior that Rozmus and Tikhonchuk and Ettehadi-Abariet al (15,16). Figure 5 shows the effects of changing the ratio values of electron density from (0.1-0.7) on the peak temperature electron values inside the plasma after its interaction with the laser pulse with different values of peak power and duration times. It has been observed that with an increase in the density ratio and laser power, the peak values of the temperature electron increase. Also, it was evident that increasing of peak electron temperature increased the duration of pulsed time. The same behavior was obtained for the results of Unnikrishnan et al (17).

Conclusions:
By inverse bremsstrahlung absorption of Nd:YAG laser pulses, the heated homogeneous plasma is studied with different values of plasma densities ratio and peak power and duration time of a pulsed laser beam. The increase in the power values of the laser pulses leads to decrease in the absorption coefficient values by a ratio of 58.3% at changing the power values from 25 to250 kW. The electron density ratio values play an important role in the interaction between the laser pulse and the plasma. So, the increases in their ratios lead to an increase in the minimum values of the absorption coefficient by 64.6% at duration pulse time 0.5 ns density ratio o.1. Also, the increase in duration time causes for a decrease in the minimum values for the absorption coefficient. On the other hand, the power values of laser pulse has a significant impact on increasing the electron temperature values by 50.0% when increasing their values from 25 to 250 kW at duration pulsed time 0.5 ns and density ratio 0.1. It is also noted that the increasing of the ratio of electron density and pulse duration time leads to increasing the peak values of the electron temperature.