Bremstrahlung Braking radiation spectra expected and total power

• fab13
In summary: No. If I have a fully ionized helium plasma, are there equal numbers of ions and electrons? What about a fully ionized oxygen plasma?I don't know, let me know it please ...If I take helium gas and fully ionize it, won't there be twice as many electrons in the plasma as ions?Since the ions have a charge of +2 and the electrons have a charge of -1?if the number of atoms in the helium gaz is constant, there will be twice more electrons than ions He++ ... ?can you give please a simple explanantion, I want to stop the game "questions/
fab13
Thread moved from the technical forums, so no Homework Template is shown
as homework, I have to do the following exercise:

Bremstrahlung emission :
We are interested in ionized plasma of density ##n##, at temperature ##T## with ions of charge number ##Z##.

1. Explain the physical origin of bremstrahlung radiation

2. Represent the expected spectra (shape and remarkable/points values)

3. Explain how the total power emitted depend of properties of plasma.

I would like to make things clearer :

1) For question 1), I saw that the bremsstrahlung radiation corresponds to the radiation emitted by a particle in deceleration, hence the name of radiation "braking".

What if the particle is accelerating: are we also talking about radiation bremsstrahlung?
Indeed, if we consider that the particle has a centripetal acceleration, as in the case of displacement in a magnetic field, we speak rather of synchrotron radiation, is that correct?

2) For question 2), we are asked to qualitatively represent the typical form of the bremsstrahlung spectra (with its points and remarkable values): someone could tell me what is this expected spectra and the values / points to to retain for this spectra (a typical spectra) ?

3) Finally, the question n ° 3) concerns the expression of the total power emitted per unit of volume, according to what I have on Wiki, this quantity is equal to :

##P_{\mathrm {Br} }[{\textrm {W/m}}^{3}]=\left[{n_{e} \over 7.69\times 10^{18}{\textrm {m}}^{-3}}\right]^{2}T_{e}[{\textrm {eV}}]^{1/2}Z_{\mathrm {eff}##

Here the formula :

The total power would then depend of : the temperature ##T## of the plasma, its density ##n## and the number of charge ##Z## of the ions of the plasma: is this correct?

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(1) In a plasma, electrons are accelerated when they make Coulomb collisions with the heavier ions. The radiation produced is considered "bremsstrahlung", whether the electron is experiencing acceleration or deceleration. This may not be linguistically correct, but this is the common usage.

(2) You should be able to find information of the spectral distribution. For example, the Wikipedia page gives the spectral distribution dP/dω.

(3) Yes, the total power depends on n^2 T^(1/2) Z, as you described.

phyzguy said:
(1) In a plasma, electrons are accelerated when they make Coulomb collisions with the heavier ions. The radiation produced is considered "bremsstrahlung", whether the electron is experiencing acceleration or deceleration. This may not be linguistically correct, but this is the common usage.

(2) You should be able to find information of the spectral distribution. For example, the Wikipedia page gives the spectral distribution dP/dω.

(3) Yes, the total power depends on n^2 T^(1/2) Z, as you described.

@phyzguy

Just a last question : shouldn't be rather ##P_{\mathrm {Br} }[{\textrm {W}}/{\textrm {m}}^{3}]={Z_{i}^{2}n_{i}n_{e} \over \left[7.69\times 10^{18}{\textrm {m}}^{-3}\right]^{2}}T_{e}[{\textrm {eV}}]^{\frac {1}{2}}## ? I mean with a ##Z^{2}## factor ?

instead of non-square powered factor ##Z## ?

By the way, where does this difference come from (between single ##Z## and ##Z^{2}## into power formula ?

Regards

In a fully ionized plasma, how do ni and ne compare? How does the formula you wrote in post #1 differ from the formula you wrote in post #3?

In the first one, I have ##\propto\,Z_{eff}## and in the post #3, I have ##\propto\,Z_{i}^2##, is there a link between ##Z_{eff}## and ##Z_{i}^{2}## ?

fab13 said:
In the first one, I have ##\propto\,Z_{eff}## and in the post #3, I have ##\propto\,Z_{i}^2##, is there a link between ##Z_{eff}## and ##Z_{i}^{2}## ?

Zeff is just the average Z for a multi-component plasma. Zi is the Z of the ion. For now let's assume the plasma is composed of only one element and Zeff=Zi=Z. You didn't answer my first question. In a fully ionized plasma, how do ni and ne compare?

normally, ##n_{i}\approx n_{e}## since the electro-neutrality, isn't it ? I don't see what you want to say, i.e about the difference between ##Z## and ##Z^2## factors into 2 expressions above ?

fab13 said:
normally, ##n_{i}\approx n_{e}## since the electro-neutrality, isn't it ?

No. If I have a fully ionized helium plasma, are there equal numbers of ions and electrons? What about a fully ionized oxygen plasma?

I don't know, let me know it please ...

If I take helium gas and fully ionize it, won't there be twice as many electrons in the plasma as ions? Since the ions have a charge of +2 and the electrons have a charge of -1?

if the number of atoms in the helium gaz is constant, there will be twice more electrons than ions He++ ... ? can you give please a simple explanantion, I want to stop the game "questions/answers" ...

fab13 said:
if the number of atoms in the helium gaz is constant, there will be twice more electrons than ions He++ ... ? can you give please a simple explanantion, I want to stop the game "questions/answers" ...
I thought I gave a simple explanation. I don't want to just tell you the answer. You need to put some effort into thinking about it. In a helium plasma ne = 2 * ni. What is the general relationship between ne and ni for a nucleus of charge Z? How does this answer your question about the difference between your two equations? If you can't answer questions like this, how do you expect to do physics?

you might want to say that ##Z_{e}=1## for electrons and ##Z_{i}=2## for ion, so ##Z_{e}\,Z_{i} = Z_{i} = Z_{eff}## ??

No, you're still not getting it. The point is that ne = Z * ni. So your first equation, which has ne^2 * Z is the same as your second equation, which has ne*ni*Z^2.

ok, thanks a lot !

so could you confirm that actually, with a full ionized gas of Helium, we have : ne = Zi ni = 2 ni :

there will be twice more electrons than ions He++ ... ?

I thought my suggestion was wrong.
?

fab13 said:
so could you confirm that actually, with a full ionized gas of Helium, we have : ne = Zi ni = 2 ni

Yes, this is correct. What would the relationship be for a fully ionized gas of oxygen?

ne = 8 ni, good ?

fab13 said:
ne = 8 ni, good ?
Correct!

What is Bremstrahlung?

Bremstrahlung, also known as braking radiation, is a type of electromagnetic radiation that is emitted when a charged particle is decelerated or deflected by another charged particle or an external electromagnetic field.

How is Bremstrahlung produced?

Bremstrahlung is produced when a charged particle, such as an electron, is accelerated or decelerated by an external force, such as an electric field. This acceleration causes the particle to emit photons, resulting in the production of Bremstrahlung radiation.

What is the Braking Radiation spectrum?

The Bremstrahlung spectrum refers to the distribution of photon energies emitted during the process of Bremstrahlung. This spectrum is continuous and ranges from low to high energies, with the majority of photons having energies in the X-ray range.

What factors affect the Bremstrahlung spectrum?

The energy of the charged particles, the strength of the external force, and the type of material the particles are interacting with can all affect the Bremstrahlung spectrum. Additionally, the energy of the emitted photons can also be influenced by the characteristics of the material, such as its density and atomic number.

What is the total power of Bremstrahlung radiation?

The total power of Bremstrahlung radiation is dependent on the energy of the charged particles and the rate at which they are decelerated. In general, the higher the energy of the charged particles, the more powerful the Bremstrahlung radiation will be. The total power can also be affected by the material the particles are interacting with and the strength of the external force.

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