based on dyson spheres.. imagine we construct an sphere of high radius R ,
then we fill the sphere with hydrogen, if the sphere is huge and the hydrogen is too then the gravity will make the particles collapse and create a sun
is this doable? fill an sphere with hydrogen an manipulate the gas to create an artificial sun in case our sun need to be replaced
Yes, if you have enough cold hydrogen it will collapse under its own gravity and become a star. If you have enough you will not need to even enclose it, since gravity will confine the gas. In fact, it is better to not confine it too much.
The problem is that warm hydrogen tends to fluff up: the atoms bounce around at a high rate, producing a larger volume and lower density. So if you start with a sphere filled with more than the Jeans mass of hydrogen it will start collapsing under its own weight. Alternatively, if you have a sphere larger than the Jeans length $$\lambda_J=\sqrt{\frac{15k_BT}{4\pi G\mu\rho}}$$ it will collapse. Note that this depends on the temperature $T$: hot gas has a larger Jeans length and you need more gas density $\rho$ to get it to collapse. Now, the total mass of hydrogen will be more than 0.075 solar masses (i.e. a lot) so there will be a lot of gravitational energy released when it starts imploding. That energy turns into temperature, and soon the collapse stops.
In space what happens is that the warm gas radiates away some heat as blackbody radiation, cools off, and implodes a bit more. If you confine it inside a too reflective sphere the energy cannot escape and the gas stays hot (this is also the mainstream idea of why dark matter halos are big and diffuse: there is no counterpart to photons for dark matter to radiate away, so they don't implode well under gravity).
How big sphere do you need? If we start with hydrogen gas ($\mu=3.32\times 10 ^{-27}$ kg) at room temperature $T=300$ K and one atmosphere $\rho=0.0899$ kg/m$^3$ I get $\lambda_J=498,000$ km. That is however just 0.0000234 solar masses (about 7.8 earth masses), so it will be a dud. It is not the Jeans length that sets the necessary radius of your container.
You need at least 0.079 solar masses to get fusion, so we can estimate using $M=(4\pi/3)R^3 \rho$ that $R=\left((3/4\pi)M/\rho\right )^{1/3}$, in this case $R=7.343$ million km. Compared to actual star formation this is an extremely small radius, but one atmosphere hydrogen is also extremely dense and 300 K rather hot, so it is an odd case.
As a Dyson sphere this is tiny, just 0.05 AU in radius. But the real problem is gathering so much gas in space, where it is far, far less dense. You will run into cooling issues long before you get to the Jeans collapse since the ideal gas law $PV=nRT$ points out that if you decrease the volume $V$ the pressure must increase proportionally or the temperature $T$ will start going up instead - as you do work to compress the gas, resisting the pressure, you will heat it. The funny thing is that nature already is supplying us with pre-compressed stars to build Dyson spheres around.
