The kinetic energy formula is mv^2/2. At the speed of 0.2c, the relativistic correction is only about 3%, so you can ignore it. Let's say you want a probe of only 2kg. At a speed of 60000km/s = 60 million m/s, the energy is 3600 x 10^12 joules or watt-seconds, which is the same as 1000 GWh. So, roughly the output of 1000 nuclear power plants for one hour. And this only if by some miracle we achieve 100% efficiency in converting electricity here on Earth in kinetic energy far out in space. We'll get back to this in a moment.
How long does the acceleration phase take? At a gentle 1g acceleration, this would be 60 million m/s divided by 10 m/s2, which is 6 million seconds, or 69 days, so a bit more than 2 months. At 1000g (mentioned in the article) it would only take 6000 seconds, or 100 minutes (1h40m). The average speed over this period is 0.1 c, so at the end of the acceleration phase, the spacecraft will be 10 min-light away from us, which is 180 mill km, or a bit more than 1 AU.
Now, lasers don't produce a perfectly collimated beam (i.e. parallel rays). The best one can achieve is the optical diffraction limit, which means an angle of divergence of 2.44 x lambda/pupil diameter. Let's say our laser has a huge diameter of 1.22 meters and we use green light (500 nm wavelength). We end up with an angle of 1 microradian. For such small angles the tangent is equal to the angle, so it's going to be 1e-6. In other words, for each 1 million meters, the beam spreads out by 1m. At 100 million kilometers, the beam spreads out by 100 kilometers. Since our spacecraft only has a diameter of 10m, it captures only 10^(-8) of the beam. Let's say you fiddle with the numbers (you use a bigger diameter laser, with a shorter wavelenght), and you reduce the divergence angle by a factor of 100. That means you still capture only 10^(-4) or less of the beam for most of the trip.
So that 1000 nuclear power station just went to 10 million power stations. By the way, you better build them in space, otherwise the poor Earth atmosphere will not be so happy about this whole business.
Ok, but let's now say you overcome all these issues. Congratulations, you just accelerated a spacecraft to 0.2c. What's out there in the vast empty space? Mostly molecules of hydrogen, and from time to time a speck of cosmic dust . Now that speck of dust is not so innocent. It can weigh as much as 100 mg [1]. 1 mg specs of dust are quite abundant. And such a tiny speck of dust is nasty, really nasty. Because it hits you at a speed of 0.2c, i.e. with an energy of mv^2/2 = 10^(-6) x (60 x 10^6)^2/2 = 0.5 x 3600 x 10^6 = 1800 MJ. For comparison, a modern American armor piercing tank shell has a weight of about 9 kg and a velocity of about 1600 m/s, so a total energy of 9 x 1.6 ^2 x 1e6/2 which is about 10 MJ. So one tiny speck of 1mg will hit you with the energy of 180 rounds of M1 Abrams.
You only have to spend 20 years with these little fellows.
The kinetic energy formula is mv^2/2. At the speed of 0.2c, the relativistic correction is only about 3%, so you can ignore it. Let's say you want a probe of only 2kg. At a speed of 60000km/s = 60 million m/s, the energy is 3600 x 10^12 joules or watt-seconds, which is the same as 1000 GWh. So, roughly the output of 1000 nuclear power plants for one hour. And this only if by some miracle we achieve 100% efficiency in converting electricity here on Earth in kinetic energy far out in space. We'll get back to this in a moment.
How long does the acceleration phase take? At a gentle 1g acceleration, this would be 60 million m/s divided by 10 m/s2, which is 6 million seconds, or 69 days, so a bit more than 2 months. At 1000g (mentioned in the article) it would only take 6000 seconds, or 100 minutes (1h40m). The average speed over this period is 0.1 c, so at the end of the acceleration phase, the spacecraft will be 10 min-light away from us, which is 180 mill km, or a bit more than 1 AU.
Now, lasers don't produce a perfectly collimated beam (i.e. parallel rays). The best one can achieve is the optical diffraction limit, which means an angle of divergence of 2.44 x lambda/pupil diameter. Let's say our laser has a huge diameter of 1.22 meters and we use green light (500 nm wavelength). We end up with an angle of 1 microradian. For such small angles the tangent is equal to the angle, so it's going to be 1e-6. In other words, for each 1 million meters, the beam spreads out by 1m. At 100 million kilometers, the beam spreads out by 100 kilometers. Since our spacecraft only has a diameter of 10m, it captures only 10^(-8) of the beam. Let's say you fiddle with the numbers (you use a bigger diameter laser, with a shorter wavelenght), and you reduce the divergence angle by a factor of 100. That means you still capture only 10^(-4) or less of the beam for most of the trip.
So that 1000 nuclear power station just went to 10 million power stations. By the way, you better build them in space, otherwise the poor Earth atmosphere will not be so happy about this whole business.
Ok, but let's now say you overcome all these issues. Congratulations, you just accelerated a spacecraft to 0.2c. What's out there in the vast empty space? Mostly molecules of hydrogen, and from time to time a speck of cosmic dust . Now that speck of dust is not so innocent. It can weigh as much as 100 mg [1]. 1 mg specs of dust are quite abundant. And such a tiny speck of dust is nasty, really nasty. Because it hits you at a speed of 0.2c, i.e. with an energy of mv^2/2 = 10^(-6) x (60 x 10^6)^2/2 = 0.5 x 3600 x 10^6 = 1800 MJ. For comparison, a modern American armor piercing tank shell has a weight of about 9 kg and a velocity of about 1600 m/s, so a total energy of 9 x 1.6 ^2 x 1e6/2 which is about 10 MJ. So one tiny speck of 1mg will hit you with the energy of 180 rounds of M1 Abrams.
You only have to spend 20 years with these little fellows.
[1] https://en.wikipedia.org/wiki/Cosmic_dust