We are trying to keep the output current under 1.5 A and the voltage difference Vin - Vout under 1 V.

 

We need to build a custom design on a small PCB with all internal components of the linear voltage regulator that withstand and can work in radiation environment.

 

I guess this kind of simulation can be done in software like LT SPICE.

 

We are trying to keep the output current under 1.5 A and the voltage difference Vin - Vout under 1 V.

and under short ciruit ?
as to can you make a LDO , thats up to your circuit.
how your going to do that without using silicon is acgood question
why your using a GaN pass is a question Im having difficulty with,
they are great as high voltage , and high temorature and high speed , but being a high current circuit, Im having difficulties seeing a radiation resistance advantage.
coukd you expand on your thinking of that ?

 

Again, apart from heat sink requirement, can a GaN based MOSFET be used instead BJT pass element in linear voltage regulator custom design with all individual internal components on the small PCB ?

Maybe, but the relationship between Vgs and Rds is extremely non-linear so you'll probably have a lot of difficulty making the control loop stable as these devices have a huge BW. Also the Rds varies significantly with junction temperature; they are designed to be run at a fixed moderately high temperature. At 1W your junction temp is going to be typically 100degC or more. This makes the linearity curve also highly dependent on external environmental influences adding to your control loop issues...