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In order to simulate pressures inside of a planetary core, we would need pressures over 1000 GPa. I researched diamond anvils, but they seem to only withstand pressures up to 770 GPa in some extreme cases. Is there any way to control this kind of pressure in a laboratory setting?

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There are some ways to achieve pressures of 1000GPa in a lab; however it is unlikely that you will ever be able to gain access to these resources. A standard diamond anvil should allow you to achieve pressures of a smaller planetary core, but it seems like you want to simulate pressures of a massive planet. Here are some of your options (based on wikipedia's Orders of magnitude (pressure) page).

  1. Extremely high-pressure laser implosion plasmas generators can achieve pressures up to 100TPa, much more pressure than you need (1TPa=1000GPa).
  2. As @andselisk stated, the NIF (National Fusion Reactor) can generate pressure of up to 5TPa.
  3. The last option is nuclear fusion; the pressures can reach between 540TPa to 6.5PPa, although I'm not really sure how well you could contain this explosion or if this counts as 'in a lab'.

In summary, there is no 'easy way' to achieve pressures like this in an ordinary lab; however there are places where it is possible to contain pressures like this.

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