Diffusion - Revision history

Abdehait: /* The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space */

2014-09-23T22:10:54Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T22:09:59Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T22:05:59Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T22:05:27Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T22:03:43Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T22:02:35Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T15:00:36Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3D-space

2014-09-23T14:59:40Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3 3D-space

2014-09-23T14:59:06Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3 3D-space

2014-09-23T14:56:35Z

The solution of the Boltzmann Equation for a steady stream of electrons in 3 3D-space

← Older revision		Revision as of 22:10, 23 September 2014
Line 170:		Line 170:


−	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>	+	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math> ,
−
	<math> \left( r' = (z^2 + \frac{D_L}{D}\rho^2)^{1/2} \right)</math>		<math> \left( r' = (z^2 + \frac{D_L}{D}\rho^2)^{1/2} \right)</math>

← Older revision		Revision as of 22:09, 23 September 2014
Line 172:		Line 172:
	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>		<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>

−	<math> \left( r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} \right)</math>	+	<math> \left( r' = (z^2 + \frac{D_L}{D}\rho^2)^{1/2} \right)</math>

← Older revision		Revision as of 22:05, 23 September 2014
Line 172:		Line 172:
	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>		<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>

−	<math> \left( r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} )\right</math>	+	<math> \left( r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} \right)</math>

← Older revision		Revision as of 22:05, 23 September 2014
Line 172:		Line 172:
	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>		<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>

−	(<math> r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} </math>)	+	<math> \left( r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} )\right</math>

@@ Line 167: / Line 167: @@
-<math> n(x,y,z)= \frac{i}{e (4\pi D)((4\pi D)^{1/2}} 2^{3/2} (\lambda_L D_L)^{1/2} (z^2 + \frac{D_L}{D}\rho^2)^{-1/4} \times   \exp{\lambda_L z} K_{1/2}[ \lambda_L(z^2 + frac{D_L}{D}\rho^2)^{1/2}] </math>
+<math> n(x,y,z)= \frac{i}{e (4\pi D)((4\pi D)^{1/2}} 2^{3/2} (\lambda_L D_L)^{1/2} (z^2 + \frac{D_L}{D}\rho^2)^{-1/4} \times   \exp{\lambda_L z} K_{1/2}[ \lambda_L(z^2 + \frac{D_L}{D}\rho^2)^{1/2}] </math>
 <math>  n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>
-(<math> r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} </math>
+(<math> r' = z^2 + \frac{D_L}{D}\rho^2)^{1/2} </math>)
 GO BACK [https://wiki.iac.isu.edu/index.php/Gaseous_Medium_Physical_Concepts#Electron_Diffusion]

← Older revision		Revision as of 15:00, 23 September 2014
Line 170:		Line 170:


−	<math> n(x,y,z)= \frac{i}{~~\exp {~~(4\pi D)} \frac {\exp{\lambda (r'- z)}{r'} </math>	+	<math> n(x,y,z)= \frac{i} {e (4\pi D)} \frac {\exp{\lambda (r'- z)}}{r'} </math>

	(<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>		(<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>

@@ Line 157: / Line 157: @@
-= The solution of the Boltzmann Equation for a steady stream of electrons in 3 3D-space=
+= The solution of the Boltzmann Equation for a steady stream of electrons in  3D-space=
@@ Line 170: / Line 170: @@
-<math>  n(x,y,z)= \frac{i}{\e {(4\pi D)} \frac {\exp{\lambda (r'- z)}{r'} </math>
+<math>  n(x,y,z)= \frac{i}{\exp {(4\pi D)} \frac {\exp{\lambda (r'- z)}{r'} </math>
 (<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>

← Older revision		Revision as of 14:59, 23 September 2014
Line 170:		Line 170:


−	<math> n(x,y,z)= \frac{i}{e (4\pi D) \exp{\~~lambda_L \frac{~~r'- z}{r'} </math>	+	<math> n(x,y,z)= \frac{i}{\e {(4\pi D)} \frac {\exp{\lambda (r'- z)}{r'} </math>

	(<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>		(<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>

← Older revision		Revision as of 14:56, 23 September 2014
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−	<math> n(x,y,z)= \frac{i}{e (4\pi D)((4\pi D)^{1/2}} 2^{3/2} (\lambda_L D_L)^{1/2} (z^2 + frac{D_L}{D}\rho^2)^{-1/4} \times </math>	+	<math> n(x,y,z)= \frac{i}{e (4\pi D)((4\pi D)^{1/2}} 2^{3/2} (\lambda_L D_L)^{1/2} (z^2 + frac{D_L}{D}\rho^2)^{-1/4} \times \exp{\lambda_L z} K_{1/2}[ \lambda_L(z^2 + frac{D_L}{D}\rho^2)^{1/2}] </math>
−
−


		+	<math> n(x,y,z)= \frac{i}{e (4\pi D) \exp{\lambda_L \frac{r'- z}{r'} </math>

		+	(<math> r' = z^2 + frac{D_L}{D}\rho^2)^{1/2} </math>

	GO BACK [https://wiki.iac.isu.edu/index.php/Gaseous_Medium_Physical_Concepts#Electron_Diffusion]		GO BACK [https://wiki.iac.isu.edu/index.php/Gaseous_Medium_Physical_Concepts#Electron_Diffusion]