I just followed the link. The trip values for the breakers are the numbers on the handles. You have at least 3 different sizes in your panel the red, blue & black (the top left one is the main 240V 100A) the blue and reds are the 120V 15 amp & 20 amp the top right is a 240V and there should be a number on the handle that is its amperage. The numbers you want are the ampacities of the breaker they should trip close to this value. the normal load for a breaker is 80% of the value on the handle. As breakers age or have been tripped many times sometimes they do trip early. If you need the curve values we need the type and brand. The type is normally something like "QP".
First, there is such a thing as a multi-wire branch circuit (MWBC), in which two hots intentionally and consensually shate a neutral. They are placed on opposite poles of service, which means only differential current flows through the neutral. This works for 2 hots in single (split) phase service, and up to 3 hots in 3-phase (208V) service which you will only find commercially or in NYC.
Neutrals must be carefully wired to be monogamous to its partner hot(s), to assure that the neutral carries no more current than its partner hot(s). After all, neutrals don't have breakers. If a neutral carried current for more than its intended hots, it could overload, and nothing would detect this. Borrowing a neutral is not allowed.
Another rule is that currents must be equal in every cable or conduit. This means no loops, wiring routes must be a strict "tree" topology. It also means the neutral will always be in the same cable with its partner hot, or hots in MWBC.
And that means MWBCs will be readily apparent in the service panel, because they will enter the box in a red-black-white cable. (or in the same conduit). When you see that, place both red and black gots on a 2-pole breaker, so that when you switch off one side, the other is also switched off. That satisfies a basic rule of MWBC.
At this point, shutting off that breaker must arrest all current flow in the neutral.
If it does not, then you have a "promiscuous neutral" problem that you should aggressively eliminate.
Grounds, on the other hand, are allowed to be promiscuous, since current only flows on them during fault conditions.
Best Answer
I don't know about "slow trip circuit breakers", but maybe I can help you understand trip curves (and circuit breakers) a bit better. Then you'll see that all circuit breakers are "slow trip".
Your basic, everyday, run of the mill circuit breaker offers two types of protection. Short-circuit protection is provided using a magnetic trip function, while overload (over-current) protection uses a thermal trip function.
Short-circuit Protection
To provide this type of protection, a circuit breaker relies on the fact that current traveling through a wire creates a magnetic field. The breaker basically uses a solenoid to open the circuit, in the event that there's a large fault current flowing. If there's enough current flowing, the magnetic field is large enough to pull open the circuit. This is often known as an instantaneous trip, because it can react in just a cycle or two (0 - 0.05 seconds).
Overcurrent Protection
This type of protection is provided using a thermal device, that works based on the fact that current traveling through a wire generates heat. As the current flowing through a wire increases, so too does the temperature of the wire. A circuit breaker uses a bi-metal strip to trip the breaker, if the temperature (current) gets too high. This is known as "long trip", or "slow trip", because it takes time for the breaker to react (0.5 - 1000 seconds).
Trip Curves
If you look at the trip curve of a breaker, you can see both types of protection in action. You'll notice a slow arcing motion leading down the chart, this is the "long time trip" portion of the chart. As the current increases, the time required for the breaker to trip decreases. Eventually, the breaker hits the instantaneous trip threshold. At this point the breaker trips within a cycle or two. This can be seen at the bottom of the chart, where the curve levels off and goes straight across the bottom of the chart.
Now that we've covered the basics, let's take a look at an example. Here's the trip curve for a 20 ampere Square-D QO circuit breaker.
Click for larger view
The vertical axis is time in seconds, and the horizontal axis is multiples of current. I've highlighted in orange what two times the breakers rating looks like (40 amperes). As you can see, even at 40 amperes this breaker shouldn't trip for about 9 to 35 seconds. This is because it's relying on the thermal protection, and the bi-metal strip has to heat enough before it pulls the circuit open.
I've also highlighted in red what it would take to trip the breaker in one second, since an observer might consider a second "instantaneous". You'll notice that it should take between 4.5 and 8 times the breakers rating, before the breaker trips in under a second. That means your saw would be pulling 90-160 amperes, when the breaker tripped.
If your saw is pulling that much current, the problem is not the breaker, it's the saw. Increasing the size of the breaker is not the solution.
Check the saw for faults, including a short-circuit. You may also want to test/replace the breaker, as breakers can go bad.
After some more research, there do seem to be what are known as "High Magnetic (HM)" circuit breakers available. Schneider Electric describes them as
One such device would be the QO120HM Miniature Circuit Breaker. I couldn't find a trip curve for this device, but rumor has it the instantaneous trip function may not kick in until 20-30 times the rated current (400-600 amperes for a 20 ampere breaker). However, I don't think these are applicable to your situation, since there's no way the saw should draw 400 amperes when starting (or at any time for that matter, unless there's a short-circuit).