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Almost all papers on plasma mentioned that plasma ions drag on a particle is in the direction is opposite to the velocity of the particle. But no one said anything about the other two components; are the other components zeroes? What about the velocity which is a vector and in any direction will always have three components which would mean three drags in opposite direction. The Plasma drag ( Morfill 1980, Gruen et. al. 1984, Northop 1989,1990,1992) is given by

$F = - 2\sqrt{\pi}b^2 n_i m_i u^2 $

$n_i$ = plasma ions density, $m_i$= masss density, $b$ = radius of the particle and $u$=relative vel0city of the particle w.r.t plasma.

Since the velocity is spherical polar coordinates is:

$\dot{r}= \vec v$ = $r\hat{r}$ + $r\dot{\phi}\hat{\theta}$ + $r\dot{\phi}\sin{\theta}\hat{\phi}, $
$v^2$ = $r^2 + r^2{\dot{\theta}^2}+ r^2\dot{\phi}\sin^2{\theta}$

can the drag force be decomposed into:

$ F_r =- 2\sqrt{\pi}b^2 n_i m_i (r^2) $;

$ F_\theta =- 2\sqrt{\pi}b^2 n_i m_i (r^2{\dot{\theta}^2})$ ;

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

If the particle is moving along the azimuthal direction is the total force equivalent to

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

Supposing, the plasma is at the origin of a Spherical polar Frame and a particle is passing through it at some radial distance, at ang co-latitude angle (θ) = 45degree and azimulth angle (ϕ) =60degree. How would one find the drag force if one is interested in the effect along the components or let say one is interested in finding the path of the particle?

Almost all papers on plasma mentioned that plasma ions drag on a particle is in the direction is opposite to the velocity of the particle. But no one said anything about the other two components; are the other components zeroes? What about the velocity which is a vector and in any direction will always have three components which would mean three drags in opposite direction. The Plasma drag ( Morfill 1980, Gruen et. al. 1984, Northop 1989,1990,1992) is given by

$F = - 2\sqrt{\pi}b^2 n_i m_i u^2 $

$n_i$ = plasma ions density, $m_i$= masss density, $b$ = radius of the particle and $u$=relative vel0city of the particle w.r.t plasma.

Since the velocity is spherical polar coordinates is:

$\dot{r}= \vec v$ = $\dot r\hat{r}$ + $r\dot{\phi}\hat{\theta}$ + $r\dot{\phi}\sin{\theta}\hat{\phi}, $
$v^2$ = $\dot r^2 + r^2{\dot{\theta}^2}+ r^2\dot{\phi}\sin^2{\theta}$

can the drag force be decomposed into:

$ F_r =- 2\sqrt{\pi}b^2 n_i m_i (\dot r^2) $;

$ F_\theta =- 2\sqrt{\pi}b^2 n_i m_i (r^2{\dot{\theta}^2})$ ;

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

If the particle is moving along the azimuthal direction is the total force equivalent to

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

Supposing, the plasma is at the origin of a Spherical polar Frame and a particle is passing through it at some radial distance, at ang co-latitude angle (θ) = 45degree and azimulth angle (ϕ) =60degree. How would one find the drag force if one is interested in the effect along the components or let say one is interested in finding the path of the particle?

Almost all papers on plasma mentioned that plasma ions drag on a particle is in the direction is opposite to the velocity of the particle. But no one said anything about the other two components; are the other components zeroes? What about the velocity which is a vector and in any direction will always have three components which would mean three drags in opposite direction. The Plasma drag ( Morfill 1980, Gruen et. al. 1984, Northop 1989,1990,1992) is given by

$F = - 2\sqrt{\pi}b^2 n_i m_i u^2 $

$n_i$ = plasma ions density, $m_i$= masss density, $b$ = radius of the particle and $u$=relative vel0city of the particle w.r.t plasma.

Since the velocity is spherical polar coordinates is:

$\dot{r}= \vec v$ = $r\hat{r}$ + $r\dot{\phi}\hat{\theta}$ + $r\dot{\phi}\sin{\theta}\hat{\phi}, $
$v^2$ = $r^2 + r^2{\dot{\theta}^2}+ r^2\dot{\phi}\sin^2{\theta}$

can the drag force be decomposed into:

$ F_r =- 2\sqrt{\pi}b^2 n_i m_i (r^2) $;

$ F_\theta =- 2\sqrt{\pi}b^2 n_i m_i (r^2{\dot{\theta}^2})$ ;

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

If the particle is moving along the azimuthal direction is the total force equivalent to

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

Almost all papers on plasma mentioned that plasma ions drag on a particle is in the direction is opposite to the velocity of the particle. But no one said anything about the other two components; are the other components zeroes? What about the velocity which is a vector and in any direction will always have three components which would mean three drags in opposite direction. The Plasma drag ( Morfill 1980, Gruen et. al. 1984, Northop 1989,1990,1992) is given by

$F = - 2\sqrt{\pi}b^2 n_i m_i u^2 $

$n_i$ = plasma ions density, $m_i$= masss density, $b$ = radius of the particle and $u$=relative vel0city of the particle w.r.t plasma.

Since the velocity is spherical polar coordinates is:

$\dot{r}= \vec v$ = $r\hat{r}$ + $r\dot{\phi}\hat{\theta}$ + $r\dot{\phi}\sin{\theta}\hat{\phi}, $
$v^2$ = $r^2 + r^2{\dot{\theta}^2}+ r^2\dot{\phi}\sin^2{\theta}$

can the drag force be decomposed into:

$ F_r =- 2\sqrt{\pi}b^2 n_i m_i (r^2) $;

$ F_\theta =- 2\sqrt{\pi}b^2 n_i m_i (r^2{\dot{\theta}^2})$ ;

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

If the particle is moving along the azimuthal direction is the total force equivalent to

$ F_\phi =- 2\sqrt{\pi}b^2 n_i m_i (r^2\dot{\phi}\sin^2{\theta}) ? $

Supposing, the plasma is at the origin of a Spherical polar Frame and a particle is passing through it at some radial distance, at ang co-latitude angle (θ) = 45degree and azimulth angle (ϕ) =60degree. How would one find the drag force if one is interested in the effect along the components or let say one is interested in finding the path of the particle?