My Solutions - Contribuições do utilizador [pt]

Plasma density distribution

2017-07-06T11:48:40Z

Ist426982:

(F. F.Chen 3.6)
An isothermal plasma is confined between the planes $x=\pm a$ in a magnetic field $\vec{B}=B_0\vec{u}_z$.
The density distribution is $n(x)=n_0\left(1-x^2/a^2\right)$.

(a) Derive an expression for the electron diamagnetic drift velocity, as a function of $x$.

(b) Draw a diagram showing the density profile and the direction of the electron diamagnetic drift on both sides of the midplane,
if $\vec{B}$ points out of the paper.

(c)Evaluate $v_D$ at $x=a/2$, if $B=0.2$ T, $kT_e=2$ eV and $a=4$ cm.

Plasma density distribution

2017-07-06T11:48:29Z

Ist426982:

Plasma density distribution

2017-07-06T11:48:12Z

Ist426982:

Plasma density distribution

2017-07-03T17:22:07Z

Ist426982: Criou a página com "(F. F.Chen 3.6) An isothermal plasma is confined between the planes $x=\pm a$ in a magnetic field $\vec{B}=B_0\vec{u}_z$. The density distribution is \(n(x)=n_0\left(1-x..."

(F. F.Chen 3.6)
An isothermal plasma is confined between the planes $x=\pm a$ in a magnetic field $\vec{B}=B_0\vec{u}_z$.
The density distribution is $n(x)=n_0\left(1-x^2/a^2\right)$.

Física e Tecnologia dos Plasmas

2017-06-22T13:14:12Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

*[[Magnitude drift]]

*[[Electron density and scale lenght]]

*[[Ion and electron drifts (earth's magnetic field)]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Magnetic mirrors / Fermi acceleration]]

*[[Magnetic mirrors / trapped particles]]

*[[Magnetic mirror / electron motion and velocity]]

*[[ E $\times$B drift ]]

*[[Drift in toroidal plasma]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Plasma density distribution]]

*[[Drifts and current density in plasma column ]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Drift in toroidal plasma

2017-06-17T16:10:29Z

Ist426982:

(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius $R=10$ cm and square cross section of size $a=1$ cm.
The magnetic fiel is generated by an electrical current $I$ along the symmetry axis.
The plasma is Maxwellian with temperature $kT=100$ eV and density $n_0=10^{19}$ m$^{-3}$.There is no applied electric field.

(a) Sketch the typical drift orbits in the non-uniform $\vec{B}$ field, for both positive ions and electrons with $v_\parallel=0$.

(b) Calculate the rate of charge accumulation (Coulomb per second) due to the curvature and gradient drifts on the upper part of the chamber.
The magnetic field in the center of the chamber is 1 T and you can use the approximation $R \gg a$ if necessary.

Drift in toroidal plasma

2017-06-17T16:10:19Z

Ist426982:

Drift in toroidal plasma

2017-06-17T16:09:57Z

Ist426982:

Drift in toroidal plasma

2017-06-17T16:08:26Z

Ist426982:

Drift in toroidal plasma

2017-06-17T16:08:11Z

Ist426982:

(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius $R=10$ cm and square cross section of size $a=1$~cm.
The magnetic fiel is generated by an electrical current $I$ along the symmetry axis.
The plasma is Maxwellian with temperature $kT=100$ eV and density $n_0=10^{19}$ m$^{-3}$.There is no applied electric field.

(a) Sketch the typical drift orbits in the non-uniform $\vec{B}$ field, for both positive ions and electrons with $v_\parallel=0$.

(b) Calculate the rate of charge accumulation (Coulomb per second) due to the curvature and gradient drifts on the upper part of the chamber.
The magnetic field in the center of the chamber is 1 T and you can use the approximation $R\gg a$ if necessary.

Drift in toroidal plasma

2017-06-17T16:07:19Z

Ist426982:

(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius $R=10$ cm and square cross section of size $a=1$~cm.
The magnetic fiel is generated by an electrical current $I$ along the symmetry axis.
The plasma is Maxwellian with temperature $kT=100$~eV and density $n_0=10^{19}$~m$^{-3}$. There is no applied electric field.

(a) Sketch the typical drift orbits in the non-uniform $\vec{B}$ field, for both positive ions and electrons with $v_\parallel=0$.

(b) Calculate the rate of charge accumulation (Coulomb per second) due to the curvature and gradient drifts on the upper part of the chamber.
The magnetic field in the center of the chamber is 1 T and you can use the approximation $R\gg a$ if necessary.

Drift in toroidal plasma

2017-06-17T16:06:55Z

Ist426982: Criou a página com "(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius $R=10$ cm and square cross section of size $a=1$~cm. The magnetic fiel is generated by..."

(F. F. ~ Chen 2.19) A plasma is created in a toroidal chamber with average radius $R=10$ cm and square cross section of size $a=1$~cm.
The magnetic fiel is generated by an electrical current $I$ along the symmetry axis.
The plasma is Maxwellian with temperature $kT=100$~eV and density \(n_0=10^{19}$~m$^{-3}$. There is no applied electric field.

(a) Sketch the typical drift orbits in the non-uniform $\vec{B}$ field, for both positive ions and electrons with $v_\parallel=0$.

(b) Calculate the rate of charge accumulation (Coulomb per second) due to the curvature and gradient drifts on the upper part of the chamber.
The magnetic field in the center of the chamber is 1 T and you can use the approximation $R\gg a$ if necessary.

E $\times$B drift

2017-06-17T16:03:16Z

Ist426982:

(D. R. Nicholson ~ 2.3) Consider a particle moving in a time-dependent electric field $\vec{E} = - \dot{E} t\vec{u}_y$, where $\dot{E}$ is a constant, and a uniform magnetic field $\vec{B}=B_0\vec{u}_z$.

(a) Calculate the $\vec{E}\times\vec{B}$ drift.

(b) Relate the resulting accelerated drift with a force and verify that the drift due to that force is the polarization drift.

E $\times$B drift

2017-06-17T16:02:46Z

Ist426982: Criou a página com "(D. R. Nicholson ~ 2.3) Consider a particle moving in a time-dependent electric field $\vec{E} = - \dot{E} t\vec{u}_y$, where $\dot{E}$ is a constant, and a uniform ma..."

(D. R. Nicholson ~ 2.3) Consider a particle moving in a time-dependent electric field
$\vec{E} = - \dot{E} t\vec{u}_y$, where $\dot{E}$ is a constant, and
a uniform magnetic field $\vec{B}=B_0\vec{u}_z$.

(a) Calculate the $\vec{E}\times\vec{B}$ drift.

(b) Relate the resulting accelerated drift with a force and verify that the drift due to that force is the polarization drift.

Magnetic mirror / electron motion and velocity

2017-06-17T15:58:36Z

Ist426982:

(F. F. ~ Chen 2.20)
The magnetic field along the axis of a magnetic mirror is $B_(z) = B_0(1+\alpha^2z^2)$, where $\alpha$ is
a constant. Suppose that at $z=0$ an electron has velocity $v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2$.

(a) Describe qualitatively the electron motion.

(b) Determine the values of $z$ where the electron is reflected.

(c) Write the equation of motion of the guiding center for the direction parallel to $\vec{B}$ and show that there is a
sinusoidal oscillation. Calcule the frequency of the motion as a function of $v$.

Magnetic mirror / electron motion and velocity

2017-06-17T15:58:03Z

Ist426982: Criou a página com "(F. F. ~ Chen 2.20) The magnetic field along the axis of a magnetic mirror is $B_(z) = B_0(1+\alpha^2z^2)$, where $\alpha$ is a constant. Suppose that at $z=0$ an electr..."

(F. F. ~ Chen 2.20)
The magnetic field along the axis of a magnetic mirror is $B_(z) = B_0(1+\alpha^2z^2)$, where $\alpha$ is
a constant. Suppose that at $z=0$ an electron has velocity $v^2 = 3 v_{\parallel}^2 = \frac{3}{2}v_{\perp}^2$.

(a) Describe qualitatively the electron motion.
(b) Determine the values of $z$ where the electron is reflected.
(c) Write the equation of motion of the guiding center for the direction parallel to $\vec{B}$ and show that there is a
sinusoidal oscillation. Calcule the frequency of the motion as a function of $v$.

Magnetic mirrors / trapped particles

2017-06-17T15:56:02Z

Ist426982: Criou a página com "(F. F.~Chen 2.11) A plasma with an isotropic distribution of speeds is placed inside a magnetic mirror with mirror ratio $R_m=4$. There are no collisions, so that the part..."

(F. F.~Chen 2.11) A plasma with an isotropic distribution of speeds is placed inside a magnetic mirror with mirror ratio $R_m=4$.
There are no collisions, so that the particles in the loss cone escape, while the others remain trapped.
Calculate the fraction of particles that remains trapped.

Magnetic mirrors / Fermi acceleration

2017-06-17T15:53:47Z

Ist426982:

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

A cosmic ray proton is trapped between two moving magnetic mirrors with
mirror ratio $R_m=5$. Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane.
Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.

(a) Using the invariance of $\mu$, find the energy to which the proton is accelerated before it escapes.

(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, ''i.e.'', treat each mirror as a flat piston and show that the velocity gained at each bounce is $2v_m$; ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably
during the acceleration process.

Magnetic mirrors / Fermi acceleration

2017-06-17T15:53:19Z

Ist426982:

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

A cosmic ray proton is trapped between two moving magnetic mirrors with
mirror ratio $R_m=5$. Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane.
Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.

(a) Using the invariance of $\mu$, find the energy to which the proton is accelerated before it escapes.

(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, ''i.e.'', treat each mirror as a flat piston and show that the velocity gained at each bounce is $2v_m$; ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably
during the acceleration process.

Magnetic mirrors / Fermi acceleration

2017-06-17T15:52:54Z

Ist426982:

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

A cosmic ray proton is trapped between two moving magnetic mirrors with
mirror ratio $R_m=5$. Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane.
Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.

(a) Using the invariance of $\mu$, find the energy to which the proton is accelerated before it escapes.

(b) How long does it take to reach that energy? Suggestions: i) suppose that the $B$ field is approxiamtely uniform in the space between the mirrors and changes abruptly near the mirrors, \textit{i.e.}, treat each mirror as a flat piston and show that the velocity gained at each bounce is $2v_m$; ii) compute the number of bounces necessary; iii) assume that the distance between the mirrors does not change appreciably
during the acceleration process.

Magnetic mirrors / Fermi acceleration

2017-06-14T16:26:34Z

Ist426982:

Magnetic mirrors / Fermi acceleration

2017-06-14T16:25:50Z

Ist426982:

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

A cosmic ray proton is trapped between two moving magnetic mirrors with
mirror ratio $R_m=5$. Initially its energy is $W=1$ keV and $v_\perp = v_\parallel$ at the midplane.
Each mirror moves toward the midplane with a velocity $v_m=10$ km/s and the initial distance between the mirrors is $L=10^{10}$ km.

Magnetic mirrors / Fermi acceleration

2017-06-14T16:10:54Z

Ist426982: Criou a página com "(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays)."

(F. F. Chen ~ 2.12, Fermi acceleration of cosmic rays).

Ion and electron drifts (earth's magnetic field)

2017-04-04T14:50:58Z

Ist426982:

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Single particle motion I
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~ 2.8) Suppose the earth's magnetic field is $3\times10^{-5}$ T at the equator and falls off as $1/r^3$ as in a perfect
dipole. Let there be an isotropic population of 1 eV protons and 30 keV electrons, each with density $n=10^7$ m$^{-3}$
at $r=5$ earth radii in the equator plane.

(a) Compute the ion and electron $\vec{\nabla} B$ drift velocities.

(b) Does an electron drift eastward or westward?

(c) How long does an electron take to encircle the earth?

(d) Compute the current ring density in A/m$^2$.

Ion and electron drifts (earth's magnetic field)

2017-04-04T14:50:36Z

Ist426982: Criou a página com "<div class="toccolours mw-collapsible mw-collapsed" style="width:420px"> '''Metadata''' <div class="mw-collapsible-content"> *CONTEXTO : Segundo ciclo universitário *AREA:..."

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Single particle motion I
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~ 2.8) Suppose the earth's magnetic field is $3\times10^{-5}$ T at the equator and falls off as $1/r^3$ as in a perfect
dipole. Let there be an isotropic population of 1 eV protons and 30 keV electrons, each with density $n=10^7$ m$^{-3}$
at $r=5$ earth radii in the equator plane.

(a) Compute the ion and electron $\vec{\nabla} B$ drift velocities.

(b) Does an electron drift eastward or westward?

(c) How long does an electron take to encircle the earth?

(d) Compute the current ring density in A/m$^2$.

Física e Tecnologia dos Plasmas

2017-04-04T14:39:39Z

Ist426982: /* Single particle motion I */

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

*[[Magnitude drift]]

*[[Electron density and scale lenght]]

*[[Ion and electron drifts (earth's magnetic field)]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Magnetic mirrors / Fermi acceleration]]

*[[Magnetic mirrors / trapped particles]]

*[[Magnetic mirror / electron motion and velocity]]

*[[ E $\times$B drift ]]

*[[Drift in toroidal plasma]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Electron density and scale lenght

2017-04-04T14:27:33Z

Ist426982:

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Debye shielding and fundamental efects
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~ 2.5) Suppose electrons obey the Boltzmann relation in a cylindrical symmetric plasma column,
$n_e(r) = n_0\exp(e\phi/kT_e)$. The electron density varies with a scale length $\lambda$, ''i.e.'',
$\partial n_e / \partial r \simeq - n_e/\lambda$.

(a) Using $\vec{E} = -\vec{\nabla}\phi$, find the radial electric field for given $\lambda$.

(b) For electrons, show that $r_L = 2\lambda$ when the $\vec{E}\times\vec{B}$ drift velocity, $v_E$, is equal to the thermal speed,
$v_{t}=\sqrt{2kT_e/m}$ (this means that the finite Larmor radius effects are important if the $\vec{E}\times\vec{B}$ drift velocity
is of the order of the thermal speed).

Electron density and scale lenght

2017-04-04T14:02:34Z

Magnitude drift

2017-03-29T18:07:53Z

Ist426982:

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Debye shielding and fundamental efects
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~2.7) An electron beam with density $n_e=10^{14}$ m$^{-3}$ and radius $R=1$ cm crosses a region with a uniform
magnetic field $\vec{B}=B_0\vec{u}_z$, where $B_0=2$ T and the $zz$ axis is aligned with the direction of propagation
of the beam. Determine the direction and magnitude of the $\vec{E}\times\vec{B}$ drift at $r=R$ (note that $\vec{E}$ is
the electrostatic field created by the charge of the beam).

Magnitude drift

2017-03-29T18:07:32Z

Ist426982:

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Debye shielding and fundamental efects
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~2.7) An electron beam with density $n_e=10^{14}$ m$^{-3}$ and radius $R=1$ cm crosses a region with a uniform
magnetic field $\vec{B}=B_0\vec{u}_z)\, where \(B_0=2)\ T and the \(zz)\ axis is aligned with the direction of propagation
of the beam. Determine the direction and magnitude of the \(\vec{E}\times\vec{B}$ drift at $r=R$ (note that $\vec{E}$ is
the electrostatic field created by the charge of the beam).

Magnitude drift

2017-03-29T18:07:13Z

<div class="toccolours mw-collapsible mw-collapsed" style="width:420px">
'''Metadata'''
<div class="mw-collapsible-content">
*CONTEXTO : Segundo ciclo universitário
*AREA: Física
*DISCIPLINA: Física e Tecnologia dos Plasmas
*ANO: 4
*LINGUA: en
*AUTOR: Vasco Guerra
*MATERIA PRINCIPAL: Debye shielding and fundamental efects
*DESCRICAO:
*DIFICULDADE: *
*TEMPO MEDIO DE RESOLUCAO: 300 [s]
*TEMPO MAXIMO DE RESOLUCAO: 600 [s]
*PALAVRAS CHAVE:
</div>
</div>

(F. F. Chen ~2.7) An electron beam with density $n_e=10^{14}$ m$^{-3}$ and radius $R=1)\ cm crosses a region with a uniform
magnetic field \(\vec{B}=B_0\vec{u}_z)\, where \(B_0=2)\ T and the \(zz)\ axis is aligned with the direction of propagation
of the beam. Determine the direction and magnitude of the \(\vec{E}\times\vec{B}$ drift at $r=R$ (note that $\vec{E}$ is
the electrostatic field created by the charge of the beam).

Física e Tecnologia dos Plasmas

2017-03-29T18:00:19Z

Ist426982: /* Single particle motion II */

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

*[[Magnitude drift]]

*[[Electron density and scale lenght]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Magnetic mirrors / Fermi acceleration]]

*[[Magnetic mirrors / trapped particles]]

*[[Magnetic mirror / electron motion and velocity]]

*[[ E $\times$B drift ]]

*[[Drift in toroidal plasma]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-29T17:59:40Z

Ist426982: /* Single particle motion II */

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

*[[Magnitude drift]]

*[[Electron density and scale lenght]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Magnetic mirrors / Fermi acceleration]]

*[[Magnetic mirrors / trapped particles]]

*[[Magnetic mirror / electron motion and velocity]]

*[[ E $\times$B drift ]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-29T17:55:24Z

Ist426982: /* Exercises */

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

*[[Magnitude drift]]

*[[Electron density and scale lenght]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Debye lenght

2017-03-26T16:23:52Z

Ist426982:

Consider Debye’s potential created by a punctual test charge $q_T$ that
is placed inside an homogeneous plasma.

a) Show that the charge in the shielding cloud exactly cancels $q_T$. Calculate the total charge inside spheres of radii $ \lambda_D/2 , \; \lambda_D$ and $ 5\lambda_D $

b)Determine the electrostatic interaction energy between the test
charge and the particles in the plasma and the total mean energy
of the plasma particles (assume $ T_e=T_i=T$ ).

<div class="toccolours mw-collapsible mw-collapsed" style="width:210px">
'''Answer'''
<div class="mw-collapsible-content">
(a)

(b)

</div>

Física e Tecnologia dos Plasmas

2017-03-26T00:46:14Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-26T00:45:47Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-26T00:45:26Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-26T00:44:46Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Debye shielding and fundamental efects==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion I==

===Exercises===

*[[Particle orbit]]

===Problems===

*[[Example of an exam problem]]

==Single particle motion II==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Fluid drifts==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in non-magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Waves in magnetized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in weakly ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and transport in fully ionized plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Kinetic theory I==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Física e Tecnologia dos Plasmas

2017-03-26T00:44:03Z

Ist426982: /* Applied plasma technology */

Física e Tecnologia dos Plasmas

2017-03-26T00:43:33Z

Ist426982: /* Plasma experiments and diagnostics */

Física e Tecnologia dos Plasmas

2017-03-26T00:43:05Z

Ist426982: /* Distribution function and kinetic theory */

Física e Tecnologia dos Plasmas

2017-03-26T00:42:45Z

Ist426982: /* Diffusion and mobility in ionized gases */

Física e Tecnologia dos Plasmas

2017-03-26T00:42:29Z

Ist426982: /* Plasma oscillations */

Física e Tecnologia dos Plasmas

2017-03-26T00:42:04Z

Ist426982: /* Maxwell's and fluid equations in plasmas */

Física e Tecnologia dos Plasmas

2017-03-26T00:41:32Z

Ist426982: /* Particle motions in uniform and nonuniform fields */

Física e Tecnologia dos Plasmas

2017-03-26T00:40:04Z

Ist426982:

Física e Tecnologia dos Plasmas

2017-03-26T00:38:33Z

Ist426982:

<div class="toclimit-1">
__TOC__
</div>

==Plasmas fundamentals==

===Exercises===

*[[Debye Shielding]]

*[[Debye lenght]]

*[[Debye shield /spherical conductor]]

*[[Plasma frequency]]

===Problems===

*[[Example of an exam problem]]

==Particle motions in uniform and nonuniform fields==

===Exercises===

*[[Particle orbit]]

===Problems===

*[[Example of an exam problem]]

==Maxwell's and fluid equations in plasmas==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Plasma oscillations==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Diffusion and mobility in ionized gases==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Distribution function and kinetic theory==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Plasma experiments and diagnostics==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

==Applied plasma technology==

===Exercises===

*[[Example of an exercise]]

===Problems===

*[[Example of an exam problem]]

Particle orbit

2017-03-02T20:06:08Z

Ist426982:

(D. R. Nicholson ~2.1)
Consider a particle of charge $q>0$ and mass $m$, initially at rest at $(x,y,z)=(0,0,0)$,
in the presence of a static magnetic field $\vec{B}=B_0\vec{u}_z$ and $\vec{E}=E_0\vec{u}_y$, with $E_0,B_0>0$.

(a) Sketch the orbit of the particle.

(b) Derive an exact expression for the orbit of the particle.

(c) Show that the orbit can be separated into an oscillatory term and a constant drift term.
After averaging in time over the oscillatory motion, is there any net acceleration?
If not, how are the forces balanced?

(d) In a neutral plasma, with positive and negative particles and ions of different masses, would there be any net current?

(e) Suppose the electric field were replaced by a gravitational force in the $yy$ direction, would there be a net current?

Particle orbit

2017-03-02T20:04:54Z

Ist426982: Criou a página com "(D. R. Nicholson ~2.1) Consider a particle of charge $q>0$ and mass $m$, initially at rest at $(x,y,z)=(0,0,0)$, in the presence of a static magnetic field \(\vec{B}=B..."

My Solutions - Contribuições do utilizador [pt]

Plasma density distribution

Plasma density distribution

Plasma density distribution

Plasma density distribution

Física e Tecnologia dos Plasmas

Drift in toroidal plasma

Drift in toroidal plasma

Drift in toroidal plasma

Drift in toroidal plasma

Drift in toroidal plasma

Drift in toroidal plasma

Drift in toroidal plasma

E \(\times\)B drift

E \(\times\)B drift

Magnetic mirror / electron motion and velocity

Magnetic mirror / electron motion and velocity

Magnetic mirrors / trapped particles

Magnetic mirrors / Fermi acceleration

Magnetic mirrors / Fermi acceleration

Magnetic mirrors / Fermi acceleration

Magnetic mirrors / Fermi acceleration

Magnetic mirrors / Fermi acceleration

Magnetic mirrors / Fermi acceleration

Ion and electron drifts (earth's magnetic field)

Ion and electron drifts (earth's magnetic field)

Física e Tecnologia dos Plasmas

Electron density and scale lenght

Electron density and scale lenght

Magnitude drift

Magnitude drift

Magnitude drift

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Debye lenght

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Física e Tecnologia dos Plasmas

Particle orbit

Particle orbit