Bremstrahlung Braking radiation spectra expected and total power

[fab13]

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?

Thanks for your help

 

[phyzguy]

(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.

 

[fab13]

(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

Thanks for your quick answer.

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

 

[phyzguy]

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?

 

[fab13]

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 $Z_{i}^{2}$ ?

 

[phyzguy]

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?

 

[fab13]

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 ?

 

[phyzguy]

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?

 

[fab13]

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

 

[phyzguy]

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?

 

[fab13]

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" ...

 

[phyzguy]

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?

 

[fab13]

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

 

[phyzguy]

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.

 

[fab13]

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.
?
Sorry for my bad english.

 

[phyzguy]

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?

 

[fab13]

ne = 8 ni, good ?

 

[phyzguy]

ne = 8 ni, good ?

Correct!