MOSCOW BAUMANN STATE TECHNICAL UNIVERSITY
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BACK

AIM OF THE WORK

SHORT THEORY

   Plasma

   Radiation by the Thermodynamic Equilibrium

   Radiation in the Conditions of the Local Thermodynamic Equilibrium

   Method of Relative Intensities

   Advisable literature

REFERENCE INFORMATION

   Spectral lines

   Argon (Ar I)

   Argon (Ar II)

   Crom (Cr I)

   Iron (Fe I)

   Hydrogen (H I)

   Mercury (Hg I)

   Calculation formulas

EQUIPMENT

   Spectrometer

   Optical behch design

   Optical resolution

   CCD-detector

   Fibre optic cable

   Collimating lens

   AVALight lamp

   SPECTROMETER CONTROL PARAMETERS

EXPERIMENT

   Experiment scheme

   Àcquaintance with control interfaces

   Order of carrying out the work

   Practical part
 
Method of Relative Intensities
Method of Relative Intensities
The temperature describing the state of optically thin plasma in the conditions of the local thermodynamic equilibrium can be defined if one measures the intensity of some line of radiated by plasma spectral lines l in absolute units on the formula:
Jki=N0(gk/g0)Akihnki exp(-Ek/kT), (11)
Where the values N0, gk, g0, gi, Aki, h, nki, Ek are taken respectively for transitions in an atom, ion or molecule. But the exact measuring of absolute intensities of spectral lines is connected with great experimental difficulties. And in many cases only relative values of probabilities of transitions are known. The spectrascopic finding out the temperature on measurings of relative intensities of spectral lines is assumed as a basis of the method of measuring of plasma temperature (Method was worked out by L.S. Ornshtein.). It gives the opportunity to avoid the measuring of absolute values and doesn't require the knowledge the absolute values of concentrations of atoms and ions. The main point of the method is the following. 2 special lines are considered which appear by transition between excited levels ki and l m of one sort of particles (atoms, ions of the given division etc.). If the occupyings of all these levels answer the distribution of Bolzman with the same temperature of excitation Òå, then having put down the expression (11) for both lines and also combining them we'll get the ratio in the form
Jki /Jlm=(Aki/Alm)(gk/gl)(llm/lki) exp[-(Ek-El)/kTe], (12)
Where lki and llm - waves lengths of chosen spectral lines. Here it is taken into consideration that the main state for the given particles of the same sort is the same. Having measured the relative intensities of 2 lines by using the formula (12) the electronic temperature can be calculated.
Let's state the value of calculation the temperature. Having differentiated we have:
DTe/Te=[kTe/(Ek-El)][D(Jki/Jlm)/(Jki/Jlm)], (13)
Hence it is seen that the exactness of calculation Te is the higher the bigger the difference of energies of upper levels: Eki- Elm. Values Eki è Elm are set by the placement of levels in the enery scheme of the data atom or ion. It is desirable to choose spectral lines which are in the convinient for measuring area of spectrum and having difference of energies of upper levels:
DElk = El -Ek³ 1 ýÂ.
It is necessary to choose lines with known values of probabilities of spontaneous transitions. The lines must have no reabsorption and they must not belong to duplets.
To raise the exactness and trustworthiness of temperature calculation Te, the similar measurings in practice are usually carried out not for 2 but for bigger quantity of lines with different DE and the working is made graphically on the base of equation:
lg(Jki/Jlm)=lg[Akigkllm/(Almgllki)]-5040(Ek-El)/Te. (14)
Having entered the designation: Pki=Akigkhnki/g0 and Plm=Alm=Almglhnlm/g0, formula (14) can be represented as:
lg(Jki/Jlm)=lg(Pki/Plm)-5040(Ek-El)/Te , (15)
Where the value Å is expressed in electrovolts. The linearness of the received diagram will indicate of the correctness of the condition (4). The tangent of angle of … allows to find out the electronic temperature on the formula:
Te=5040(El-Ek)/[lg(Jki/Jlm) + lg(Plm/Pki)] =
= 5040(El-Ek)/[lg(Jki /Jlm)+lg[Almgmlki/(Akigkllm)]]. (16)
By the photoelectric registration of the light stream the value lg(Jki/Jlm) is calculated taking into account the spectral sensitivity FEM.
Instead of probability of spontaneous transitions Aki the power of oscillatorfikis often entered, which shows the efficiency of real atoms to absorption of energy quanta on regard for classical oscillators.
Using the connection of power of oscillator fik with the probability of transition fik=(gk/gl)e0mec3Aki/2pe2n2ki , formula (14) by photoelectric registration is written down in a such way:
lg(Vki/Vlm)=lg[fikgil2lmSlm/(fmlgml2 kiSik)] - 5040(Ek-El)/Te, (17)

ãäå Vki è Vlm, Ski è Slm - voltages at the output of the booster of direct current in the max. of intensity and spectral sensitivities for waves lengths of transitions ki è lm respectively.