Strangest Star known is the 'Talk of Astronomy'

Charles Cagle writes:
[ ... ]
In article , Craig Markwardt
wrote:
A nitpicker would be concerned with minutiae. My expression showed
that, based on the understanding of thermal gases, the ratio in
question would indeed change significantly with temperature (as
described above), and so your criticism is baseless.

CM

Nonsense. Your understanding of thermal gases has no relationship to
reality if you ignore the fact that low mass gases (which can be
completely ionized) will change the behavior of the gas with respect to
the effect of elementary particles overlapping in momentum space.

On the contrary, the Maxwell Boltzmann distribution of thermal gases
has been tested in many experimental scenarios over the past decades,
and even centuries. It speaks directly the question of the velocity
distribution of gas atoms, and hence the proportion of gas atoms which
overlap in velocity space. The ionization state or mass of the is
largely irrelevant to the temperature dependence of the distribution.
I showed that the temperature has a large effect on the ratio of
overlaps, and you continue not to address this point.

CM

In article , Craig Markwardt
wrote:

Charles Cagle writes:
[ ... ]
In article , Craig Markwardt
wrote:
A nitpicker would be concerned with minutiae. My expression showed
that, based on the understanding of thermal gases, the ratio in
question would indeed change significantly with temperature (as
described above), and so your criticism is baseless.

CM

Nonsense. Your understanding of thermal gases has no relationship to
reality if you ignore the fact that low mass gases (which can be
completely ionized) will change the behavior of the gas with respect to
the effect of elementary particles overlapping in momentum space.

On the contrary, the Maxwell Boltzmann distribution of thermal gases
has been tested in many experimental scenarios over the past decades,
and even centuries. It speaks directly the question of the velocity
distribution of gas atoms, and hence the proportion of gas atoms which
overlap in velocity space. The ionization state or mass of the is
largely irrelevant to the temperature dependence of the distribution.
I showed that the temperature has a large effect on the ratio of
overlaps, and you continue not to address this point.

CM

Okay. Let's address it then. According to the Maxwell Boltzmann
distribution of thermal gases we see that as temperature increases that
there is a wider range of velocities available to the particles of the
gas. But also there is a higher collision rate. For a wider range of
velicities we might easily see that this translates into a change of
the ratio of pairs of nuclei which are overlapping in momentum space
vs. the pairs of nuclei which are not overlapping in momentum space.
In this case we see that a temperature rise would lead to change in the
ratio so that fewer pairs would be overlapping in momentum space. On
the other side of the coin we see that each particle will undergo more
collisions per fixed unit of time. So, I'll agree that as temperature
increases that the ratio between the two type of pairs becomes more
extreme and this would cause the number of fusion reactions to fall
with a temperature increase. But a temperature increase also means
that a the nuclei will also be ionized a greater percentage of the
time. And ionization is an important factor for nuclear fusion
according to my modeling. Next, the average velocity is higher and
this means that the particles in the confined gas will be undergoing
collisions at a higher rate than they would at a lower temperature. It
is evident that the higher collsion rate will lead to more 'states' per
fixed unit of time for each particle and even with a more extreme ratio
of the types of pairs it seems obvious that the higher collision rate
because it generates more 'states' per fixed unit of time will lead to
an increase in the number of fusion reactions per fixed unit of time.
So, I don't find it unusual that more fusion reaction per fixed unit of
time will take place with an increase in temperature. But I still say
that increasing the temperature will not decrease the ratio of the
types of pairs. I previously stated that an increase in temperature
would not change the ratio of pairs to a significant degree. And in
fact I have at times stated that an increase in temperature wouldn't
effect the ratio. It is obvious that an increase in temperature will
cause some change in the ratio which translates into a more extreme
ratio. One might think that my model would predict fewer fusion
reactions by raising the temperature because the ratio has become more
extreme. But I'm saying that the fact that more states per unit of
time per particle are evolved with a higher temperature contributes to
an increase in the number of fusion reactions per fixed unit of time
even with an increase in the ratio between the two types of pairs.
This only reifies my point that one cannot change the ratio in favor of
more fusion reactions. In other words if the ratio were to decrease
then one could expect more fusion reactions per unit of time that was
keyed to say the mean free path time of flight.

I've always agreed that increasing the temperature of a confined fusion
fuel gas would lead to an increase in the number of fusion reactions
per fixed unit of time but that the standard analysis of the fusion
reaction event itself has always been flawed. I stand by my claim that
the only way to build a working nuclear fusion reactor that can reach
the 'ignited' state is to build one which can significantly lower (or
actually invert) the ratio between the two types of pairs.

Charles Cagle

Charles Cagle writes:

In article , Craig Markwardt
wrote:
...
On the contrary, the Maxwell Boltzmann distribution of thermal gases
has been tested in many experimental scenarios over the past decades,
and even centuries. It speaks directly the question of the velocity
distribution of gas atoms, and hence the proportion of gas atoms which
overlap in velocity space. The ionization state or mass of the is
largely irrelevant to the temperature dependence of the distribution.
I showed that the temperature has a large effect on the ratio of
overlaps, and you continue not to address this point.

CM

Okay. Let's address it then. According to the Maxwell Boltzmann
distribution of thermal gases we see that as temperature increases that
there is a wider range of velocities available to the particles of the
gas. But also there is a higher collision rate. For a wider range of
velicities we might easily see that this translates into a change of
the ratio of pairs of nuclei which are overlapping in momentum space
vs. the pairs of nuclei which are not overlapping in momentum space.
In this case we see that a temperature rise would lead to change in the
ratio so that fewer pairs would be overlapping in momentum space. On
the other side of the coin we see that each particle will undergo more
collisions per fixed unit of time. So, I'll agree that as temperature
increases that the ratio between the two type of pairs becomes more
extreme and this would cause the number of fusion reactions to fall
with a temperature increase. But a temperature increase also means
that a the nuclei will also be ionized a greater percentage of the
time. And ionization is an important factor for nuclear fusion
according to my modeling. Next, the average velocity is higher and
this means that the particles in the confined gas will be undergoing
collisions at a higher rate than they would at a lower temperature.

1. Using the Maxwell Boltzmann distribution I determined the exact
fraction of a gas overlaps within a certain velocity range, and is
proportional to 1/v = 1/sqrt(T).

2. Using straightforward ideal gas physics, the rate of collisions per
unit time scales as v = sqrt(T)

3. At the temperatures and densities present in contemporary fusion
experiments, the atoms are totally ionized (ionization potential
~14 eV, plasma temperature 5000 eV). Therefore your comment
about change in ionization with temperature are irrelevant.

Therefore, the increase in collision rate is offset exactly by the
dilution in velocity space, and your model would incorrectly predict
no change with temperature.

CM

In article , Craig Markwardt
wrote:

Charles Cagle writes:

In article , Craig Markwardt
wrote:
...
On the contrary, the Maxwell Boltzmann distribution of thermal gases
has been tested in many experimental scenarios over the past decades,
and even centuries. It speaks directly the question of the velocity
distribution of gas atoms, and hence the proportion of gas atoms which
overlap in velocity space. The ionization state or mass of the is
largely irrelevant to the temperature dependence of the distribution.
I showed that the temperature has a large effect on the ratio of
overlaps, and you continue not to address this point.

CM

Okay. Let's address it then. According to the Maxwell Boltzmann
distribution of thermal gases we see that as temperature increases that
there is a wider range of velocities available to the particles of the
gas. But also there is a higher collision rate. For a wider range of
velicities we might easily see that this translates into a change of
the ratio of pairs of nuclei which are overlapping in momentum space
vs. the pairs of nuclei which are not overlapping in momentum space.
In this case we see that a temperature rise would lead to change in the
ratio so that fewer pairs would be overlapping in momentum space. On
the other side of the coin we see that each particle will undergo more
collisions per fixed unit of time. So, I'll agree that as temperature
increases that the ratio between the two type of pairs becomes more
extreme and this would cause the number of fusion reactions to fall
with a temperature increase. But a temperature increase also means
that a the nuclei will also be ionized a greater percentage of the
time. And ionization is an important factor for nuclear fusion
according to my modeling. Next, the average velocity is higher and
this means that the particles in the confined gas will be undergoing
collisions at a higher rate than they would at a lower temperature.

1. Using the Maxwell Boltzmann distribution I determined the exact
fraction of a gas overlaps within a certain velocity range, and is
proportional to 1/v = 1/sqrt(T).

2. Using straightforward ideal gas physics, the rate of collisions per
unit time scales as v = sqrt(T)

3. At the temperatures and densities present in contemporary fusion
experiments, the atoms are totally ionized (ionization potential
~14 eV, plasma temperature 5000 eV). Therefore your comment
about change in ionization with temperature are irrelevant.

Therefore, the increase in collision rate is offset exactly by the
dilution in velocity space, and your model would incorrectly predict
no change with temperature.

CM

Nonsense. A totally ionized gas doesn't emit radiation. The light
from an ionized gas is produced as electrons are being acquired by
nuclei. A dilution in velocity space doesn't offset an increase in
collsion space. Where the hell's your head?

Charles Cagle

Charles Cagle wrote:


Nonsense. A totally ionized gas doesn't emit radiation. The light
from an ionized gas is produced as electrons are being acquired by
nuclei. A dilution in velocity space doesn't offset an increase in
collsion space. Where the hell's your head?

"velocity space" ????