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'''Plasma oscillations''', also known as "'''Langmuir waves'''" (after [[Irving Langmuir]]), are rapid oscillations of the [[electron density]] in conducting media such as [[Plasma (physics)|plasmas]] or [[metal]]s. The oscillations can be described as an instability in the [[Free electron model#Dielectric function of the electron gas|dielectric function of a free electron gas]]. The frequency only depends weakly on the wavelength of the oscillation. The [[quasiparticle]] resulting from the [[Quantization (physics)|quantization]] of these oscillations is the [[plasmon]].
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Langmuir waves were discovered by American [[physics|physicists]] [[Irving Langmuir]] and [[Lewi Tonks]] in the 1920s.  They are parallel in form to [[Jeans Instability|Jeans instability]] waves, which are caused by gravitational instabilities in a static medium.
 
== Explanation ==
 
Consider an electrically neutral plasma in equilibrium, consisting of a gas of positively charged [[ion]]s and negatively charged [[electrons]]. If one displaces by a tiny amount all of the electrons with respect to the ions, the [[Coulomb force]] pulls the electrons back, acting as a restoring force.
 
=== 'Cold' electrons ===
 
If the thermal motion of the electrons is ignored, it is possible to show that the charge density oscillates at the ''plasma frequency'' <br>
: <math>\omega_{pe} = \sqrt{\frac{n_e e^{2}}{m^*\varepsilon_0}}, \left[rad/s\right]</math> ([[SI units]]),
: <math> \omega_{pe} = \sqrt{\frac{4 \pi n_e e^{2}}{m^*}},</math> ([[Centimetre gram second system of units|cgs units]]),
 
where ''<math>n_e</math> '' is the number density of electrons, ''e'' is the [[electric charge]], ''m''<sup>*</sup> is the [[effective mass (solid-state physics)|effective mass]] of the electron, and
<math>\varepsilon_0</math> is the [[permittivity of free space]]. Note that the above [[formula]] is derived under the [[approximation]] that the ion mass is infinite. This is generally a good approximation, as the electrons are so much lighter than ions. (One must modify this expression in the case of electron-[[positron]] plasmas, often encountered in [[astrophysics]]).<ref>{{cite book|last=Fu|first=Ying|title=Optical properties of nanostructures|year=2011|publisher=Pan Stanford|pages=201}}</ref> Since the [[frequency]] is independent of the [[wavelength]], these [[oscillation]]s have an [[Infinity|infinite]] [[phase velocity]] and zero [[group velocity]].
 
Note that, if <math>m^*</math> is electron mass <math>(m^*=m_e)</math>, plasma frequency <math>\omega_{pe}</math> depends only on [[physical constant]]s and concentration of electrons <math>n_e</math>. The numeric expression for plasma ordinary frequency
 
:<math>f_{pe}=\omega_{pe}/2\pi</math>
is
:<math>f_{pe} \approx 8980 \sqrt{n_e} </math> Hz
with number density <math>n_e</math> in cm<sup>−3</sup>.
 
=== 'Warm' electrons ===
 
When the effects of the [[electron]] thermal speed <math>v_{e,th} = \sqrt{\frac{k_B T_{\mathrm{e}}}{m_e}}</math> are taken into account, the electron pressure acts as a restoring force as well as the electric field and the oscillations propagate with frequency and [[wavenumber]] related by the longitudinal Langmuir<ref>*{{Citation |last=Andreev |first=A. A. |title=An Introduction to Hot Laser Plasma Physics |year=2000 |publisher= Nova Science Publishers, Inc. |location=Huntington, New York |isbn=1-56072-803-5}}</ref> wave:
 
:<math>
\omega^2 =\omega_{pe}^2 +\frac{3k_BT_{\mathrm{e}}}{m_e}k^2=\omega_{pe}^2 + 3 k^2 v_{\mathrm{e,th}}^2
</math>,
called the [[David Bohm|Bohm]]-[[Eugene P. Gross|Gross]] [[dispersion relation]]. If the spatial scale is large compared to the [[Debye length]], the [[oscillation]]s are only weakly modified by the [[pressure]] term, but at small scales the pressure term dominates and the waves become dispersionless with a speed of <math>\sqrt{3} \cdot v_{e,th}</math>. For such waves, however, the electron thermal speed is comparable to the [[phase velocity]], i.e.,
:<math>
v \sim v_{ph} \ \stackrel{\mathrm{def}}{=}\  \frac{\omega}{k},
</math>
so the plasma waves can [[accelerate]] electrons that are moving with speed nearly equal to the phase velocity of the wave. This process often leads to a form of collisionless damping, called [[Landau damping]]. Consequently, the large-''k'' portion in the [[dispersion relation]] is difficult to observe and seldom of consequence.
 
In a [[bounded function|bounded]] plasma, fringing electric fields can result in propagation of plasma oscillations, even when the electrons are cold.
 
In a [[metal]] or [[semiconductor]], the effect of the [[ion]]s' periodic potential must be taken into account. This is usually done by using the electrons' [[effective mass (solid-state physics)|effective mass]] in place of ''m''.
 
== See also ==
* [[Waves in plasmas]]
* [[plasmon]]
* [[Surface plasmon resonance]]
* [[Upper hybrid oscillation]], in particular for a discussion of the modification to the mode at propagation angles oblique to the magnetic field
* In 2006, plasma physicists at the Universities of Texas and Michigan were able to photograph Langmuir waves, generated by a 30 TW laser pulse, for the first time.<ref>[http://www.eurekalert.org/pub_releases/2006-10/aps-fwe_1102706.php Fastest waves ever photographed]</ref>
*[[Electron wake]]
* [[List of plasma (physics) articles]]
 
==References==
{{Reflist}}
 
==Further reading==
*{{Citation |last=Longair |first=Malcolm S. |title=Galaxy Formation |year=1998 |publisher=Springer |location=Berlin |isbn=3-540-63785-0 }}
*{{Citation |last=Andreev |first=A. A. |title=An Introduction to Hot Laser Plasma Physics |year=2000 |publisher= Nova Science Publishers, Inc. |location=Huntington, New York |isbn=1-56072-803-5}}
 
[[Category:Waves in plasmas]]
[[Category:Plasma physics]]

Latest revision as of 23:42, 3 December 2014

If you have the desire to procedure settings instantaneously, loading files rapidly, however, the body is logy plus torpid, what would we do? If you are a giant "switchboard" that is deficiency of efficient administration program and efficient housekeeper, what would we do? If you have send the exact commands to a notice, however, the body cannot do correctly, what would we do? Yes! You require a full-featured repair registry!

Carry out window's system restore. It is really important to do this considering it removes wrong changes that have happened in the system. Some of the mistakes result from inability of the system to create restore point regularly.

The error is basically a outcome of problem with Windows Installer package. The Windows Installer is a tool used to install, uninstall plus repair the most programs on your computer. Let us discuss a few points that helped a lot of folks whom facing the similar matter.

Fixing tcpip.sys blue screen is easy to do with registry repair software.Trying to fix windows blue screen error on your is tricky because if you remove or damage the registry it may result serious damage to a computer. The registry must be cleaned and all erroneous and incomplete information removed to stop blue screen mistakes from occurring.The advantage of registry repair software is not limited to merely getting rid of the blue screen on business.You may be surprised at the better plus more improved speed plus performance of the computer system after registry cleaning is performed. Registry cleaning could really develop your computer's working abilities, incredibly whenever we choose a certain registry repair software that is especially effective.

Another widespread cause of PC slow down is a corrupt registry. The registry is a fairly important component of computers running on Windows platform. When this gets corrupted the PC will slowdown, or worse, not begin at all. Fixing the registry is easy with the utilize of a program plus tuneup utilities.

The key reason why I might not make my PC run faster was the system registry and it being fragmented. So software to defragment or clean the registry are needed. Such software are called registry cleaners. Like all additional software, there are paid ones and free ones with their blessings and disadvantages. To choose amongst the two is the user's choice.

Your disk requires area in order to run smoothly. By freeing up certain area from a disk, you are able to accelerate the PC a bit. Delete all file in the temporary internet files folder, recycle bin, well-defined shortcuts plus icons from a desktop which we never employ and remove programs you never use.

Next, there is an simple method to deal with this issue. You are able to install a registry cleaner which there are it found on the internet. This software could help you see out these errors inside a computer plus clean them. It also may figure out these malware and other threats that influence the speed of your computer. So this software will speed up PC simpler. We can choose 1 of these methods to accelerate you computer.

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